Ex:
Find the L.C.M. of 90 and 168.
Sol:
By resolving each one of the given numbers as the product of prime factors, we get:
| 90 | = | 2 × 3 × 3 × 5 |
| = | 2 × 32 × 5 | |
| 168 | = | 2 × 2 × 2 × 3 × 7 |
| = | 23 × 3 × 7 |
In these prime factorizations,
For 90: the prime factor 3 occurs twice, 2 occurs once and 5 occurs once.
For 168: the prime factor 2 occurs thrice, 3 occurs once and 7 occurs once.
We have to take the product of all the different prime factors each raised to highest power that appear in the
prime factorization of any of the two numbers.
| ∴ L.C.M. | = | 23 × 32 × 5 × 7 |
| = | 8 × 9 × 5 × 7 | |
| = | 2520 |