Least Common Multiple (LCM) of 61 and 112
The least common multiple (LCM) of 61 and 112 is 6832.
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 112?
First, calculate the GCD of 61 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 112 = 0 remainder 61 |
| 2 | 112 ÷ 61 = 1 remainder 51 |
| 3 | 61 ÷ 51 = 1 remainder 10 |
| 4 | 51 ÷ 10 = 5 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 17 | 884 |
| 107 and 173 | 18511 |
| 132 and 90 | 1980 |
| 152 and 61 | 9272 |
| 164 and 31 | 5084 |