Least Common Multiple (LCM) of 157 and 61
The least common multiple (LCM) of 157 and 61 is 9577.
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 61?
First, calculate the GCD of 157 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 61 = 2 remainder 35 |
| 2 | 61 ÷ 35 = 1 remainder 26 |
| 3 | 35 ÷ 26 = 1 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 36 | 252 |
| 140 and 37 | 5180 |
| 58 and 45 | 2610 |
| 129 and 184 | 23736 |
| 114 and 29 | 3306 |