Least Common Multiple (LCM) of 53 and 157
The least common multiple (LCM) of 53 and 157 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 53 and 157?
First, calculate the GCD of 53 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 157 = 0 remainder 53 |
| 2 | 157 ÷ 53 = 2 remainder 51 |
| 3 | 53 ÷ 51 = 1 remainder 2 |
| 4 | 51 ÷ 2 = 25 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 140 | 560 |
| 199 and 101 | 20099 |
| 166 and 31 | 5146 |
| 112 and 138 | 7728 |
| 177 and 14 | 2478 |