Least Common Multiple (LCM) of 76 and 34
The least common multiple (LCM) of 76 and 34 is 1292.
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 34?
First, calculate the GCD of 76 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 34 = 2 remainder 8 |
| 2 | 34 ÷ 8 = 4 remainder 2 |
| 3 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 105 | 4830 |
| 181 and 76 | 13756 |
| 125 and 103 | 12875 |
| 142 and 149 | 21158 |
| 153 and 11 | 1683 |