Least Common Multiple (LCM) of 136 and 107
The least common multiple (LCM) of 136 and 107 is 14552.
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 136 and 107?
First, calculate the GCD of 136 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 107 = 1 remainder 29 |
| 2 | 107 ÷ 29 = 3 remainder 20 |
| 3 | 29 ÷ 20 = 1 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 117 | 2574 |
| 100 and 133 | 13300 |
| 144 and 135 | 2160 |
| 40 and 52 | 520 |
| 123 and 156 | 6396 |