Least Common Multiple (LCM) of 84 and 137
The least common multiple (LCM) of 84 and 137 is 11508.
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 84 and 137?
First, calculate the GCD of 84 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 137 = 0 remainder 84 |
| 2 | 137 ÷ 84 = 1 remainder 53 |
| 3 | 84 ÷ 53 = 1 remainder 31 |
| 4 | 53 ÷ 31 = 1 remainder 22 |
| 5 | 31 ÷ 22 = 1 remainder 9 |
| 6 | 22 ÷ 9 = 2 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 131 | 16637 |
| 179 and 161 | 28819 |
| 114 and 197 | 22458 |
| 48 and 171 | 2736 |
| 91 and 98 | 1274 |