Least Common Multiple (LCM) of 157 and 90
The least common multiple (LCM) of 157 and 90 is 14130.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 157 and 90?
First, calculate the GCD of 157 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 90 = 1 remainder 67 |
| 2 | 90 ÷ 67 = 1 remainder 23 |
| 3 | 67 ÷ 23 = 2 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 192 | 14784 |
| 165 and 30 | 330 |
| 196 and 57 | 11172 |
| 132 and 24 | 264 |
| 128 and 106 | 6784 |