Least Common Multiple (LCM) of 138 and 87
The least common multiple (LCM) of 138 and 87 is 4002.
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 138 and 87?
First, calculate the GCD of 138 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 87 = 1 remainder 51 |
| 2 | 87 ÷ 51 = 1 remainder 36 |
| 3 | 51 ÷ 36 = 1 remainder 15 |
| 4 | 36 ÷ 15 = 2 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 10 | 940 |
| 103 and 72 | 7416 |
| 78 and 98 | 3822 |
| 156 and 194 | 15132 |
| 120 and 77 | 9240 |