Least Common Multiple (LCM) of 107 and 136
The least common multiple (LCM) of 107 and 136 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 107 and 136?
First, calculate the GCD of 107 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 136 = 0 remainder 107 |
| 2 | 136 ÷ 107 = 1 remainder 29 |
| 3 | 107 ÷ 29 = 3 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 41 | 615 |
| 106 and 106 | 106 |
| 184 and 196 | 9016 |
| 55 and 192 | 10560 |
| 93 and 114 | 3534 |