Least Common Multiple (LCM) of 132 and 157
The least common multiple (LCM) of 132 and 157 is 20724.
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 132 and 157?
First, calculate the GCD of 132 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 157 = 0 remainder 132 |
| 2 | 157 ÷ 132 = 1 remainder 25 |
| 3 | 132 ÷ 25 = 5 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 62 | 4340 |
| 142 and 119 | 16898 |
| 87 and 174 | 174 |
| 200 and 139 | 27800 |
| 36 and 196 | 1764 |