Least Common Multiple (LCM) of 56 and 157
The least common multiple (LCM) of 56 and 157 is 8792.
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 56 and 157?
First, calculate the GCD of 56 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 157 = 0 remainder 56 |
| 2 | 157 ÷ 56 = 2 remainder 45 |
| 3 | 56 ÷ 45 = 1 remainder 11 |
| 4 | 45 ÷ 11 = 4 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 20 | 1460 |
| 198 and 184 | 18216 |
| 141 and 16 | 2256 |
| 177 and 137 | 24249 |
| 167 and 92 | 15364 |