Least Common Multiple (LCM) of 77 and 126
The least common multiple (LCM) of 77 and 126 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 77 and 126?
First, calculate the GCD of 77 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 126 = 0 remainder 77 |
| 2 | 126 ÷ 77 = 1 remainder 49 |
| 3 | 77 ÷ 49 = 1 remainder 28 |
| 4 | 49 ÷ 28 = 1 remainder 21 |
| 5 | 28 ÷ 21 = 1 remainder 7 |
| 6 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 150 | 6450 |
| 140 and 190 | 2660 |
| 89 and 88 | 7832 |
| 55 and 33 | 165 |
| 109 and 78 | 8502 |