Least Common Multiple (LCM) of 76 and 102
The least common multiple (LCM) of 76 and 102 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 76 and 102?
First, calculate the GCD of 76 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 102 = 0 remainder 76 |
| 2 | 102 ÷ 76 = 1 remainder 26 |
| 3 | 76 ÷ 26 = 2 remainder 24 |
| 4 | 26 ÷ 24 = 1 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 123 | 5289 |
| 22 and 93 | 2046 |
| 27 and 161 | 4347 |
| 143 and 181 | 25883 |
| 155 and 115 | 3565 |