Least Common Multiple (LCM) of 120 and 157
The least common multiple (LCM) of 120 and 157 is 18840.
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 120 and 157?
First, calculate the GCD of 120 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 157 = 0 remainder 120 |
| 2 | 157 ÷ 120 = 1 remainder 37 |
| 3 | 120 ÷ 37 = 3 remainder 9 |
| 4 | 37 ÷ 9 = 4 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 121 | 2178 |
| 142 and 110 | 7810 |
| 148 and 61 | 9028 |
| 31 and 79 | 2449 |
| 104 and 41 | 4264 |