Least Common Multiple (LCM) of 157 and 58
The least common multiple (LCM) of 157 and 58 is 9106.
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 58?
First, calculate the GCD of 157 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 58 = 2 remainder 41 |
| 2 | 58 ÷ 41 = 1 remainder 17 |
| 3 | 41 ÷ 17 = 2 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 197 | 20685 |
| 12 and 87 | 348 |
| 116 and 52 | 1508 |
| 83 and 87 | 7221 |
| 134 and 76 | 5092 |