Least Common Multiple (LCM) of 157 and 113
The least common multiple (LCM) of 157 and 113 is 17741.
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 113?
First, calculate the GCD of 157 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 113 = 1 remainder 44 |
| 2 | 113 ÷ 44 = 2 remainder 25 |
| 3 | 44 ÷ 25 = 1 remainder 19 |
| 4 | 25 ÷ 19 = 1 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 53 | 8745 |
| 139 and 55 | 7645 |
| 119 and 115 | 13685 |
| 86 and 31 | 2666 |
| 107 and 138 | 14766 |