Least Common Multiple (LCM) of 108 and 136
The least common multiple (LCM) of 108 and 136 is 3672.
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 108 and 136?
First, calculate the GCD of 108 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 136 = 0 remainder 108 |
| 2 | 136 ÷ 108 = 1 remainder 28 |
| 3 | 108 ÷ 28 = 3 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 43 | 5676 |
| 39 and 117 | 117 |
| 44 and 133 | 5852 |
| 136 and 178 | 12104 |
| 30 and 31 | 930 |