Least Common Multiple (LCM) of 137 and 147
The least common multiple (LCM) of 137 and 147 is 20139.
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 137 and 147?
First, calculate the GCD of 137 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 147 = 0 remainder 137 |
| 2 | 147 ÷ 137 = 1 remainder 10 |
| 3 | 137 ÷ 10 = 13 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 52 | 1092 |
| 149 and 67 | 9983 |
| 147 and 147 | 147 |
| 108 and 96 | 864 |
| 127 and 119 | 15113 |