Least Common Multiple (LCM) of 87 and 100
The least common multiple (LCM) of 87 and 100 is 8700.
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 100?
First, calculate the GCD of 87 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 100 = 0 remainder 87 |
| 2 | 100 ÷ 87 = 1 remainder 13 |
| 3 | 87 ÷ 13 = 6 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 105 | 4515 |
| 144 and 130 | 9360 |
| 156 and 62 | 4836 |
| 53 and 127 | 6731 |
| 62 and 94 | 2914 |