Least Common Multiple (LCM) of 135 and 37
The least common multiple (LCM) of 135 and 37 is 4995.
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 135 and 37?
First, calculate the GCD of 135 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 37 = 3 remainder 24 |
| 2 | 37 ÷ 24 = 1 remainder 13 |
| 3 | 24 ÷ 13 = 1 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 32 | 2272 |
| 200 and 37 | 7400 |
| 170 and 42 | 3570 |
| 139 and 72 | 10008 |
| 85 and 23 | 1955 |