Least Common Multiple (LCM) of 157 and 132
The least common multiple (LCM) of 157 and 132 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 157 and 132?
First, calculate the GCD of 157 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 132 = 1 remainder 25 |
| 2 | 132 ÷ 25 = 5 remainder 7 |
| 3 | 25 ÷ 7 = 3 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 72 | 8712 |
| 195 and 14 | 2730 |
| 34 and 101 | 3434 |
| 198 and 145 | 28710 |
| 36 and 71 | 2556 |