Least Common Multiple (LCM) of 42 and 157
The least common multiple (LCM) of 42 and 157 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 42 and 157?
First, calculate the GCD of 42 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 157 = 0 remainder 42 |
| 2 | 157 ÷ 42 = 3 remainder 31 |
| 3 | 42 ÷ 31 = 1 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 53 | 848 |
| 187 and 40 | 7480 |
| 16 and 140 | 560 |
| 198 and 164 | 16236 |
| 21 and 163 | 3423 |