Least Common Multiple (LCM) of 157 and 135
The least common multiple (LCM) of 157 and 135 is 21195.
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 135?
First, calculate the GCD of 157 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 135 = 1 remainder 22 |
| 2 | 135 ÷ 22 = 6 remainder 3 |
| 3 | 22 ÷ 3 = 7 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 31 | 2542 |
| 104 and 147 | 15288 |
| 190 and 102 | 9690 |
| 50 and 198 | 4950 |
| 109 and 129 | 14061 |