Least Common Multiple (LCM) of 132 and 137
The least common multiple (LCM) of 132 and 137 is 18084.
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 137?
First, calculate the GCD of 132 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 137 = 0 remainder 132 |
| 2 | 137 ÷ 132 = 1 remainder 5 |
| 3 | 132 ÷ 5 = 26 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 91 | 2275 |
| 39 and 180 | 2340 |
| 130 and 110 | 1430 |
| 122 and 39 | 4758 |
| 153 and 91 | 13923 |