Least Common Multiple (LCM) of 136 and 157
The least common multiple (LCM) of 136 and 157 is 21352.
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 136 and 157?
First, calculate the GCD of 136 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 157 = 0 remainder 136 |
| 2 | 157 ÷ 136 = 1 remainder 21 |
| 3 | 136 ÷ 21 = 6 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 32 | 544 |
| 188 and 17 | 3196 |
| 113 and 35 | 3955 |
| 113 and 154 | 17402 |
| 125 and 155 | 3875 |