Least Common Multiple (LCM) of 101 and 87
The least common multiple (LCM) of 101 and 87 is 8787.
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 101 and 87?
First, calculate the GCD of 101 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 87 = 1 remainder 14 |
| 2 | 87 ÷ 14 = 6 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 126 | 126 |
| 101 and 68 | 6868 |
| 59 and 110 | 6490 |
| 165 and 92 | 15180 |
| 31 and 89 | 2759 |