Least Common Multiple (LCM) of 56 and 77
The least common multiple (LCM) of 56 and 77 is 616.
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 56 and 77?
First, calculate the GCD of 56 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 77 = 0 remainder 56 |
| 2 | 77 ÷ 56 = 1 remainder 21 |
| 3 | 56 ÷ 21 = 2 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 31 | 527 |
| 30 and 45 | 90 |
| 108 and 174 | 3132 |
| 55 and 109 | 5995 |
| 124 and 76 | 2356 |