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 |
|---|---|
| 112 and 86 | 4816 |
| 41 and 70 | 2870 |
| 174 and 14 | 1218 |
| 152 and 127 | 19304 |
| 22 and 42 | 462 |