Page 166 - New Medley 5 Semester 1

∴ LCM of 12 and 18 = 2 × 2 × 3 × 3 = 36 (Take two 2s
and two 3s)

To find the LCM using this method, observe how many
times each prime factor appears in the given numbers and

take maximum times a factor present in any number.

Example 7: Find the LCM of 40, 60 and 75 by the common division
method.

Solution: Write all the numbers in a row, separating them using

commas. Think of a prime, starting from the smallest
prime, that can divide at least any two given numbers

exactly. Divide the numbers and write the quotients just
below them.

If the number is not divisible, write it as it 2 40, 60,75

is.
2 20, 30,75
Continue this process, till the row contains 3 10, 15,75
two numbers divisible by the stame prime.
5 10, 5, 25

Now, the product of all the primes you 2, 1, 5
thought and the numbers left at bottom
row will be the LCM of the given numbers.

∴ LCM of 40, 60 and 75 = 2 × 2 × 3 × 5 × 2 × 5 = 600

EXERCISE 3.5

A. Find the LCM of the following numbers using the prime factorisation
method.

1. 16, 20 2. 15, 20 3. 18, 27 4. 24, 60

5. 20, 30, 50 6. 28, 42, 63 7. 48, 56, 72 8. 60, 90, 150

B. Find the LCM of the following numbers using the common multiple
method.

1. 3, 7 2. 8, 12 3. 10, 15 4. 8, 28

5. 6, 10 6. 8, 12 7. 12, 15 8. 15, 20

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