Least Common Multiple (LCM) of 102 and 15
The least common multiple (LCM) of 102 and 15 is 510.
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 102 and 15?
First, calculate the GCD of 102 and 15 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 15 = 6 remainder 12 |
| 2 | 15 ÷ 12 = 1 remainder 3 |
| 3 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 51 | 1479 |
| 178 and 65 | 11570 |
| 70 and 156 | 5460 |
| 174 and 37 | 6438 |
| 60 and 107 | 6420 |