Least Common Multiple (LCM) of 126 and 78
The least common multiple (LCM) of 126 and 78 is 1638.
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 126 and 78?
First, calculate the GCD of 126 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 78 = 1 remainder 48 |
| 2 | 78 ÷ 48 = 1 remainder 30 |
| 3 | 48 ÷ 30 = 1 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 152 | 1976 |
| 126 and 34 | 2142 |
| 72 and 75 | 1800 |
| 36 and 34 | 612 |
| 135 and 77 | 10395 |