Least Common Multiple (LCM) of 117 and 135
The least common multiple (LCM) of 117 and 135 is 1755.
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 117 and 135?
First, calculate the GCD of 117 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 135 = 0 remainder 117 |
| 2 | 135 ÷ 117 = 1 remainder 18 |
| 3 | 117 ÷ 18 = 6 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 51 | 2652 |
| 57 and 18 | 342 |
| 21 and 117 | 819 |
| 96 and 141 | 4512 |
| 58 and 150 | 4350 |