Least Common Multiple (LCM) of 76 and 126
The least common multiple (LCM) of 76 and 126 is 4788.
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 126?
First, calculate the GCD of 76 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 126 = 0 remainder 76 |
| 2 | 126 ÷ 76 = 1 remainder 50 |
| 3 | 76 ÷ 50 = 1 remainder 26 |
| 4 | 50 ÷ 26 = 1 remainder 24 |
| 5 | 26 ÷ 24 = 1 remainder 2 |
| 6 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 128 | 6784 |
| 40 and 160 | 160 |
| 101 and 53 | 5353 |
| 183 and 129 | 7869 |
| 84 and 74 | 3108 |