Least Common Multiple (LCM) of 101 and 136
The least common multiple (LCM) of 101 and 136 is 13736.
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 101 and 136?
First, calculate the GCD of 101 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 136 = 0 remainder 101 |
| 2 | 136 ÷ 101 = 1 remainder 35 |
| 3 | 101 ÷ 35 = 2 remainder 31 |
| 4 | 35 ÷ 31 = 1 remainder 4 |
| 5 | 31 ÷ 4 = 7 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 118 | 10502 |
| 68 and 198 | 6732 |
| 119 and 76 | 9044 |
| 172 and 109 | 18748 |
| 117 and 80 | 9360 |