Least Common Multiple (LCM) of 108 and 57
The least common multiple (LCM) of 108 and 57 is 2052.
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 108 and 57?
First, calculate the GCD of 108 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 57 = 1 remainder 51 |
| 2 | 57 ÷ 51 = 1 remainder 6 |
| 3 | 51 ÷ 6 = 8 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 91 | 11284 |
| 65 and 136 | 8840 |
| 102 and 193 | 19686 |
| 16 and 70 | 560 |
| 56 and 175 | 1400 |