Least Common Multiple (LCM) of 87 and 137
The least common multiple (LCM) of 87 and 137 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 87 and 137?
First, calculate the GCD of 87 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 137 = 0 remainder 87 |
| 2 | 137 ÷ 87 = 1 remainder 50 |
| 3 | 87 ÷ 50 = 1 remainder 37 |
| 4 | 50 ÷ 37 = 1 remainder 13 |
| 5 | 37 ÷ 13 = 2 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 191 | 19482 |
| 90 and 152 | 6840 |
| 187 and 90 | 16830 |
| 140 and 159 | 22260 |
| 11 and 19 | 209 |