Least Common Multiple (LCM) of 57 and 136
The least common multiple (LCM) of 57 and 136 is 7752.
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 57 and 136?
First, calculate the GCD of 57 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 136 = 0 remainder 57 |
| 2 | 136 ÷ 57 = 2 remainder 22 |
| 3 | 57 ÷ 22 = 2 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 168 | 1680 |
| 154 and 13 | 2002 |
| 13 and 47 | 611 |
| 63 and 78 | 1638 |
| 138 and 29 | 4002 |