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 |
|---|---|
| 190 and 27 | 5130 |
| 165 and 50 | 1650 |
| 65 and 148 | 9620 |
| 67 and 29 | 1943 |
| 160 and 191 | 30560 |