Least Common Multiple (LCM) of 136 and 159
The least common multiple (LCM) of 136 and 159 is 21624.
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 159?
First, calculate the GCD of 136 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 159 = 0 remainder 136 |
| 2 | 159 ÷ 136 = 1 remainder 23 |
| 3 | 136 ÷ 23 = 5 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 67 | 8643 |
| 50 and 84 | 2100 |
| 55 and 196 | 10780 |
| 122 and 10 | 610 |
| 137 and 76 | 10412 |