Least Common Multiple (LCM) of 157 and 42
The least common multiple (LCM) of 157 and 42 is 6594.
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 157 and 42?
First, calculate the GCD of 157 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 42 = 3 remainder 31 |
| 2 | 42 ÷ 31 = 1 remainder 11 |
| 3 | 31 ÷ 11 = 2 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 50 | 1400 |
| 41 and 129 | 5289 |
| 29 and 199 | 5771 |
| 38 and 113 | 4294 |
| 192 and 88 | 2112 |