Least Common Multiple (LCM) of 87 and 149
The least common multiple (LCM) of 87 and 149 is 12963.
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 149?
First, calculate the GCD of 87 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 149 = 0 remainder 87 |
| 2 | 149 ÷ 87 = 1 remainder 62 |
| 3 | 87 ÷ 62 = 1 remainder 25 |
| 4 | 62 ÷ 25 = 2 remainder 12 |
| 5 | 25 ÷ 12 = 2 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 89 | 1691 |
| 50 and 106 | 2650 |
| 80 and 107 | 8560 |
| 188 and 16 | 752 |
| 180 and 67 | 12060 |