Least Common Multiple (LCM) of 49 and 77
The least common multiple (LCM) of 49 and 77 is 539.
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 49 and 77?
First, calculate the GCD of 49 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 77 = 0 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 |
|---|---|
| 126 and 112 | 1008 |
| 45 and 115 | 1035 |
| 22 and 40 | 440 |
| 42 and 194 | 4074 |
| 142 and 153 | 21726 |