Least Common Multiple (LCM) of 157 and 53
The least common multiple (LCM) of 157 and 53 is 8321.
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 53?
First, calculate the GCD of 157 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 53 = 2 remainder 51 |
| 2 | 53 ÷ 51 = 1 remainder 2 |
| 3 | 51 ÷ 2 = 25 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 65 | 11895 |
| 145 and 39 | 5655 |
| 128 and 187 | 23936 |
| 55 and 43 | 2365 |
| 96 and 182 | 8736 |