Least Common Multiple (LCM) of 61 and 104
The least common multiple (LCM) of 61 and 104 is 6344.
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 61 and 104?
First, calculate the GCD of 61 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 104 = 0 remainder 61 |
| 2 | 104 ÷ 61 = 1 remainder 43 |
| 3 | 61 ÷ 43 = 1 remainder 18 |
| 4 | 43 ÷ 18 = 2 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 188 | 14852 |
| 51 and 64 | 3264 |
| 91 and 21 | 273 |
| 100 and 88 | 2200 |
| 98 and 82 | 4018 |