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The product obtained in above step is the required least common multiple
(L.C.M.).

Example 12 : Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.
Solution : Resolving each given number into its prime factors :
3 9 3 15
9 = 3 × 3
3 3 5 5
15 = 3 × 5
1 1

The product of each factor the greatest number of times it occurs in either number.
3 × 3 × 5 = 45.

Example 13 : Find L.C.M of 504 and 594 by prime factorization method.

Solution : To find the LCM, multiply all prime factors. But the common factors are included
only once.
2 504 2 594
2 252 3 297

2 126 3 99
3 63 3 33
3 21 11 11

7 7 1
1

504 = 2 × 2 × 2 × 3 × 3 × 7

594 = 2 × 3 × 3 × 3 × 11
2 × 2 × 2 × 3 × 3 × 3 × 7 × 11 = 16632.
The required least common multiple (L.C.M.) of 504 and 594 = 16632.

2. LCM by using Division Method

To find Least Common Multiple by using Division Method we need to follow the
following steps.

1. Write the given numbers in a horizontal line, separating them by commas.
2. Divide them by a suitable prime number, which exactly divides at least two of

the given numbers.
3. We put the quotient directly under the numbers in the next row. If the number
is not divided exactly, we bring it down in the next row.

4. We continue the process of step 2 and step 3 until all co-prime numbers are left
in the last row.

5. We multiply all the prime numbers by which we have divided and the co-prime
numbers left in the last row. This product is the least common multiple of the
given numbers.

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Mathematics In Focus - 5