Least Common Multiple (LCM) of 37 and 135
The least common multiple (LCM) of 37 and 135 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 37 and 135?
First, calculate the GCD of 37 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 135 = 0 remainder 37 |
| 2 | 135 ÷ 37 = 3 remainder 24 |
| 3 | 37 ÷ 24 = 1 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 75 | 10650 |
| 123 and 164 | 492 |
| 27 and 36 | 108 |
| 33 and 157 | 5181 |
| 168 and 81 | 4536 |