Least Common Multiple (LCM) of 61 and 110
The least common multiple (LCM) of 61 and 110 is 6710.
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 110?
First, calculate the GCD of 61 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 110 = 0 remainder 61 |
| 2 | 110 ÷ 61 = 1 remainder 49 |
| 3 | 61 ÷ 49 = 1 remainder 12 |
| 4 | 49 ÷ 12 = 4 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 100 | 700 |
| 57 and 67 | 3819 |
| 96 and 33 | 1056 |
| 96 and 169 | 16224 |
| 102 and 185 | 18870 |