SSC CGL HCF AND LCM MCQ ENGLISH

Correct Answer : (A)

Explanation : Given:Product of 2 co-prime numbers =956Product of 2 numbers = Product of their LCM and HCFlet the two co-prime numbers be ‘ a ‘ and ‘ b ‘.So, a×b= LCM (a,b)× HCF (a,b)It is given that a and b are co-prime, so their HCF =1So, from the above given equation, we getLCM (a,b)=a×b=956∴956 is the required LCM of 2 co-prime number.

Correct Answer : (C)

Explanation : Given:The number must be divisible by 8,10,12 and 16 .The concept of LCM is used.LCM of 8,10,12 and 16 is 240 .The smallest 4− digit number is 1,000 .Now,1000÷240Q=4R=40⇒240−40=200⇒1000+200=1200∴1200 is 4 digit the smallest number which is divisible by 8,10,12 and 16 .

Correct Answer : (B)

Explanation : Given:The ratio of the two numbers is 3:4 .Their LCM is 480 .Product of two numbers = HCF × LCMLet the numbers be 3x and 4x .Here x is the HCF of the two numbers.Now,3x×4x=480×x⇒12×2=480x⇒x=40∴ Their HCF is 40 .

Correct Answer : (A)

Explanation : We know that,Second number = LCM ×HCF First Number=72×1224=36∴ Difference between two numbers =36−24=12

Correct Answer : (C)

Explanation : Given:HCF =6LCM =864One number =96Second number = ?Let, the second number is x .LCM × HCF = First number × Second number⇒864×6=96×x⇒x=864×696⇒x=54

Correct Answer : (A)

Explanation : Given:HCF = 24LCM = 168Ratio of numbers = 1 ∶ 7As we know,Product of numbers = LCM × HCFLet numbers be x and 7x.x × 7x = 24 × 168⇒ x2 = 24 × 24⇒ x = 24∴ Larger number = 7x = 24 × 7 = 168

Correct Answer : (D)

Explanation : Given:Polynomial f(x)=x6−3×4+3×2−1And polynomial g(x)=x3+3×2+3x+1As we know,(x2−y2)=(x+1)(x−y)According to the question, we havef(x)=x6−3×4+3×2−1=x6−x4−2×4+2×2+x2−1=x4(x2−1)−2×2(x2−1)+1(x2+1)=(x2−1)(x4−2×2+1)=(x+1)(x−1)(x4−2×2+1)=(x+1)(x−1)(x2−1)2=(x+1)(x−1)(x+1)2(x−1)2=(x+1)3(x−1)3…(1)And,g(x)=x3+3×2+3x+1=x3+x2+2×2+2x+x+1=x2(x+1)+2x(x+1)+1(x+1)=(x+1)(x2+2x+1)=(x+1)(x+1)2=(x+1)3…(2)Now,The HCF of f(x) and g(x) is the common factor of equations (1) and (2)=(x+1)3∴ The HCF of the polynomials x6−3×4+3×2−1 and x3+3×2+3x+1 is (x+1)3 .

Correct Answer : (A)

Explanation : Given:24×34×53×72 and 22×36×55HCF by Prime Factorization Method24×34×53×72 and 22×36×55If we calculate the HCF of these two numbersthen we can see highest common factors are 22×34×53∴ Required HCF is 22×34×53

Correct Answer : (C)

Explanation : Given:144,360 and 504HCF (Highest Common Factor) of two or more numbers is the greatest factor that divides the numbers.144=24×32360=23×32×5504=23×32×7Thus, HCF (144,360,504)=23×32=72∴72 is the HCF of 144,360 , and 504 .

Correct Answer : (D)

Explanation : Given:HCF =14LCM =3920First number =490Product of the two numbers = HCF × LCMLet the second number be N .⇒490×N=14×3920⇒N=392035⇒N=112∴ The second number is 112 .

Correct Answer : (C)

Explanation : Given:LCM of two numbers =1237LCM × HCF = one number × another number1237 is a prime number, soPossible numbers are =1237 and 1⇒LCM×HCF= product of two numbersPutting the values, we get,⇒1237×HCF=1237×1⇒HCF=1∴ HCF of two integers is 1 .

Correct Answer : (D)

Explanation : HCF of 18 and 15=3LCM of 18 and 15=90∴ Product of HCF and LCM of both numbers =3×90=270

Correct Answer : (B)

Explanation : Given,HCF and LCM of two numbers are 13 and 1989 respectivelyOne of the numbers is 117First number × Second number =HCF×LCMLet the second number be m⇒117×m=13×1989⇒m=13×1989117⇒m=221

Correct Answer : (B)

Explanation : Given:LCM of two numbers =2376HCF of two numbers =33One of the number =297∵ (HCF of two numbers )×( LCM of two numbers )=( First number )×( Second number )∴ Second number =33×2376297=264

Correct Answer : (C)

Explanation : Given:8,24,36,54LCM is the Least Common Multiples of all the given numbers.8=2324=23×336=22×3254=2×33Least common multiple of 8,24,36,54 is 23×33⇒8×27⇒216∴ The LCM of 8,24,36,54 is 216 .

Correct Answer : (A)

Explanation : Let two numbers are 98x and 98y .Then,Product of number = Product of HCF and LCM98x×98y=98×2352⇒xy=24Let x=8 and y=3 (As Co-prime factors of 24 by 8 and 3 )Then, Sum of number =98×8+98×3=98(11)=1078

Correct Answer : (D)

Explanation : Given:(t2−3t−4)=(t2−4t+t−4)=(t−4)(t+1)(t2+5t−6)=(t2+6t+t−6)=(t−1)(t+6)(t2−1)=(t+1)(t−1)∴ HCF is 1.

Correct Answer : (A)

Explanation : Given,HCF of two numbers =7As we know,LCM = HCF × Co – Prime numberLCM should always will be divisible by HCF.Option (A):161÷7Quotient =23Remainder =0Option (B):872÷7Quotient =124Remainder =4Option (C):587÷7Quotient =83Remainder =6Option (D):697÷7Quotient =99Remainder =6∴ LCM of these 2 number is 161 .

Correct Answer : (A)

Explanation : Concept used:Here we will use LCMCalculation:First find the factors of⇒12=22×31⇒15=31×51⇒18=21×32⇒20=22×51LCM =22×32×51To make it a perfect square we need to multiply it by 5 .=22×32×52=900∴ The correct answer is 900 .

Correct Answer : (C)

Explanation : Given:HCF=3LCM=90Calculation:Let assume the number be 3aand the second number be 3bAccording to question,3a+3b=33⇒a+b=11 ………(1)LCM of 3a3b=3abSo, 3ab=90⇒ab=30 …(2)From equation (1) and equation (2)a=5b=6⇒ The first number is =3a=3×5=15⇒ The second number is =3b=3×6=18The difference of reciprocal of numbers115−118=190

Correct Answer : (D)

Explanation : Given:Two brands of chocolate available =24 and 15LCM of two or more numbers is the smallest number which is a common multiple of the given numberAccording to the question,Factors of 24=2×2×2×3Factors of 15=3×5LCM of (25,15)=23×3×5⇒120Number of boxes of a pack of 24=12024⇒5Number of boxes of a pack of 15=12015⇒8∴ The number of boxes of both brands of chocolates is 5 and 8 .

Correct Answer : (B)

Explanation : Given:The greatest number of four digits that is divisible by 30,36,45 , and 75 :Using the L.C.M. method,LCM of (30,36,45,75)=900⇒2×2×3×3×5×5The greatest number of four digits is 9999 .The greatest number of four-digit which is exactly divisible by 30,36,45,75=9999−99=9900

Correct Answer : (C)

Explanation : Given:Product of two numbers =6912 and HCF =24We know that,Product of two number = HCF × LCM∴ LCM =691224=288

Correct Answer : (A)

Explanation : Factor of 726=2×3×11×11Factor of 426=2×3×7×11So, HCF (726,426)=2×3×11=66

Correct Answer : (B)

Explanation : Given:Sum of two numbers = 528H.C.F. = 33Let two numbers be 33x and 33y where x and y are prime to each other.Accordingly,33x + 33y = 528⇒ 33(x + y) = 528⇒ x + y = 16So, The number of such pairs is (1, 15) (3, 13) (5, 11) (7, 9) where x and y are prime to each other.∴ The number of such pairs is 4.

Correct Answer : (C)

Explanation : Given:The numbers =81,243,54HCF = Smallest power of the shared factors of given numbers⇒81=34⇒243=35⇒54=33×2There is a shared factor is 3 and the smallest power of three is 33 .The HCF of (81,243,54)=33=27

Correct Answer : (A)

Explanation : Factor of 15=3×5Factor of 175=5×5×7So, LCM =3×5×5×7=525

Correct Answer : (C)

Explanation : Factorization of 36 : 23621839331 Factorization of 84 : 28424232177136=22×3284=22×3×7∴ H.C.F. =22×3=12

Correct Answer : (D)

Explanation : Given:The HCF of 1683,2244 , and 5049 is x .HCF – The greatest number which divides each of the two or more numbers⇒1683=3×3×11×17⇒2244=2×2×3×11×17⇒5049=3×3×3×11×17The HCF =(3×11×17)⇒561So,⇒x=561Now,The sum of digits of x=(5+6+1)⇒12∴ The required sum of digits of x is 12 .

Correct Answer : (B)

Explanation : Concept:Bring the denominators of the powers of all the numbers to same.Calculation:LCM of the denominators 4,3,6,2 is 12The numbers can be written as3312,2412,5212,2612∵ All the powers have denominators same,33,24,52,2624 is the least of them.∴213 is least of them.