Least Common Multiple (LCM) of 61 and 113
The least common multiple (LCM) of 61 and 113 is 6893.
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 113?
First, calculate the GCD of 61 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 113 = 0 remainder 61 |
| 2 | 113 ÷ 61 = 1 remainder 52 |
| 3 | 61 ÷ 52 = 1 remainder 9 |
| 4 | 52 ÷ 9 = 5 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 66 | 4620 |
| 76 and 165 | 12540 |
| 140 and 171 | 23940 |
| 11 and 24 | 264 |
| 150 and 79 | 11850 |