Least Common Multiple (LCM) of 123 and 87
The least common multiple (LCM) of 123 and 87 is 3567.
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 123 and 87?
First, calculate the GCD of 123 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 87 = 1 remainder 36 |
| 2 | 87 ÷ 36 = 2 remainder 15 |
| 3 | 36 ÷ 15 = 2 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 141 | 5640 |
| 105 and 186 | 6510 |
| 99 and 175 | 17325 |
| 92 and 112 | 2576 |
| 100 and 100 | 100 |