Least Common Multiple (LCM) of 126 and 77
The least common multiple (LCM) of 126 and 77 is 1386.
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 77?
First, calculate the GCD of 126 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 77 = 1 remainder 49 |
| 2 | 77 ÷ 49 = 1 remainder 28 |
| 3 | 49 ÷ 28 = 1 remainder 21 |
| 4 | 28 ÷ 21 = 1 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 119 | 11900 |
| 110 and 73 | 8030 |
| 104 and 183 | 19032 |
| 29 and 198 | 5742 |
| 133 and 186 | 24738 |