Least Common Multiple (LCM) of 57 and 156
The least common multiple (LCM) of 57 and 156 is 2964.
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 156?
First, calculate the GCD of 57 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 156 = 0 remainder 57 |
| 2 | 156 ÷ 57 = 2 remainder 42 |
| 3 | 57 ÷ 42 = 1 remainder 15 |
| 4 | 42 ÷ 15 = 2 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 105 | 9870 |
| 20 and 100 | 100 |
| 12 and 170 | 1020 |
| 21 and 186 | 1302 |
| 132 and 116 | 3828 |