Least Common Multiple (LCM) of 101 and 157
The least common multiple (LCM) of 101 and 157 is 15857.
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 101 and 157?
First, calculate the GCD of 101 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 157 = 0 remainder 101 |
| 2 | 157 ÷ 101 = 1 remainder 56 |
| 3 | 101 ÷ 56 = 1 remainder 45 |
| 4 | 56 ÷ 45 = 1 remainder 11 |
| 5 | 45 ÷ 11 = 4 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 135 | 2970 |
| 85 and 114 | 9690 |
| 198 and 123 | 8118 |
| 83 and 187 | 15521 |
| 106 and 99 | 10494 |