Least Common Multiple (LCM) of 135 and 152
The least common multiple (LCM) of 135 and 152 is 20520.
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 152?
First, calculate the GCD of 135 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 152 = 0 remainder 135 |
| 2 | 152 ÷ 135 = 1 remainder 17 |
| 3 | 135 ÷ 17 = 7 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 88 | 2376 |
| 110 and 109 | 11990 |
| 89 and 49 | 4361 |
| 144 and 66 | 1584 |
| 118 and 16 | 944 |