Least Common Multiple (LCM) of 157 and 180
The least common multiple (LCM) of 157 and 180 is 28260.
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 180?
First, calculate the GCD of 157 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 180 = 0 remainder 157 |
| 2 | 180 ÷ 157 = 1 remainder 23 |
| 3 | 157 ÷ 23 = 6 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 119 | 9520 |
| 90 and 86 | 3870 |
| 165 and 94 | 15510 |
| 118 and 117 | 13806 |
| 182 and 78 | 546 |