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# Solved Examples(Set 2) - HCF and LCM

 6. The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is: A. 20 B. 28 C. 24 D. 30

Explanation:

Product of two numbers = Product of their HCF and LCM.

Let one number $=x$

=> $25 × x = 5 × 150$

=> $x=\dfrac{5 × 150}{25}=30$

 7. 504 can be expressed as a product of primes as A. 2 × 2 × 2 × 3 × 3 × 7 B. 2 × 3 × 3 × 3 × 3 × 7 C. 2 × 2 × 3 × 3 × 7 × 7 D. 2 × 3 × 3 × 3 × 7 × 7

Explanation:

It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7

 8. Which of the following integers has the most number of divisors? A. 99 B. 101 C. 182 D. 176

Explanation:

99 = 1 × 3 × 3 × 11
=> Divisors of 99 are 1, 3, 11, 9, 33 and 99

101 = 1 × 101
=> Divisors of 101 are 1 and 101

182 = 1 × 2 × 7 × 13
=> Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182

176 = 1 × 2 × 2 × 2 × 2 × 11
=> Divisors of 176 are 1, 2, 11, 4, 22, 8, 44, 16, 88, 176

Hence 176 has most number of divisors.

 9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is A. 32 B. 42 C. 41 D. 37

Explanation:

LCM of 3, 5, 7 and 8 = 840

28523 ÷ 840 = 33 remainder = 803

Hence the least number which should be added = 840 - 803 = 37

 10. What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22 ? A. 1386 B. 1216 C. 1286 D. 1436

Explanation:

LCM of 12, 14, 18 and 22 = 2772

Hence the least number which will be exactly divisible by 12, 14, 18 and 22 = 2772

2772 ÷ 2 = 1386

1386 is the number which when doubled, we get 2772

Hence, 1386 is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22.