Least Common Multiple (LCM) of 47 and 136
The least common multiple (LCM) of 47 and 136 is 6392.
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 47 and 136?
First, calculate the GCD of 47 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 136 = 0 remainder 47 |
| 2 | 136 ÷ 47 = 2 remainder 42 |
| 3 | 47 ÷ 42 = 1 remainder 5 |
| 4 | 42 ÷ 5 = 8 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 93 | 10416 |
| 65 and 129 | 8385 |
| 164 and 106 | 8692 |
| 131 and 106 | 13886 |
| 63 and 89 | 5607 |