Page 79 - Maths Class 04

Let us find the LCM of 30 and 45.

One way to find the least common multiple (LCM) of two numbers is to first

list the prime factors of each number.

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Then, multiply each factor the greatest number of times it occurs in any of

the given numbers. If the same factor occurs more than once in both the
numbers, you multiply the factor the greatest number of times it occurs.

2 : one occurrence

3 : two occurrence

5 : one occurrence

LCM = 2 × 3 × 3 × 5 = 90

Relationship Between HCF and LCM

Product of two given numbers is equal to the product of their HCF and LCM.

HCF of two numbers × LCM of two numbers = Product of two numbers

or

HCF = Product of two numbers ÷ LCM

or

LCM = Product of two numbers ÷ HCF

Example : Find the LCM if product of two numbers is 168 and their HCF is 4.

Solution : HCF × LCM = product of two numbers.

\LCM = product of two numbers ÷ HCF

= 168 ÷ 4

= 42

\The LCM is 42.

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