Least Common Multiple (LCM) of 137 and 87
The least common multiple (LCM) of 137 and 87 is 11919.
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 87?
First, calculate the GCD of 137 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 87 = 1 remainder 50 |
| 2 | 87 ÷ 50 = 1 remainder 37 |
| 3 | 50 ÷ 37 = 1 remainder 13 |
| 4 | 37 ÷ 13 = 2 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 191 | 20437 |
| 185 and 166 | 30710 |
| 108 and 66 | 1188 |
| 180 and 15 | 180 |
| 178 and 180 | 16020 |