Least Common Multiple (LCM) of 157 and 60
The least common multiple (LCM) of 157 and 60 is 9420.
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 60?
First, calculate the GCD of 157 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 60 = 2 remainder 37 |
| 2 | 60 ÷ 37 = 1 remainder 23 |
| 3 | 37 ÷ 23 = 1 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 200 | 16600 |
| 86 and 178 | 7654 |
| 123 and 176 | 21648 |
| 42 and 116 | 2436 |
| 81 and 101 | 8181 |