Least Common Multiple (LCM) of 102 and 76
The least common multiple (LCM) of 102 and 76 is 3876.
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 76?
First, calculate the GCD of 102 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 76 = 1 remainder 26 |
| 2 | 76 ÷ 26 = 2 remainder 24 |
| 3 | 26 ÷ 24 = 1 remainder 2 |
| 4 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 73 | 3723 |
| 48 and 133 | 6384 |
| 148 and 59 | 8732 |
| 74 and 10 | 370 |
| 83 and 166 | 166 |