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Topic Question Set

Q 21 :

If the product of two numbers a and b is 1152 and HCF of a and b is 12, then LCM of a and b is:

  • 88

     

  • 90

     

  • 92

     

  • 96

     

(4)

We have, a × b = 1152 and HCF (a, b) = 12We know that LCM (a, b) × HCF (a, b) = a × b⇒ LCM (a, b) × 12 = 1152⇒ LCM (a, b) = 1152 ÷ 12 = 96

Q 22 :

What is the least number that is divisible by all the numbers from 1 to 10?

  • 420

     

  • 840

     

  • 2520

     

  • 3200

     

(3)  

For any number to be divisible by all the numbers from 1 to 10, we need LCM of the numbers from 1 to 10. So, it must have maximum powers of each prime number that can be obtained in prime factorisation of numbers from 1 to 10.

∴ 1 = 12 = 2¹3 = 3¹4 = 2²5 = 5¹6 = 2¹ × 3¹7 = 7¹8 = 2³9 = 3²10 = 2¹ × 5¹So, required least number = 2³ × 3² × 5¹ × 7¹ = 8 × 9 × 5 × 7 = 2520