Least Common Multiple (LCM) of 61 and 133
The least common multiple (LCM) of 61 and 133 is 8113.
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 133?
First, calculate the GCD of 61 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 133 = 0 remainder 61 |
| 2 | 133 ÷ 61 = 2 remainder 11 |
| 3 | 61 ÷ 11 = 5 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 105 | 3045 |
| 32 and 180 | 1440 |
| 134 and 98 | 6566 |
| 182 and 15 | 2730 |
| 125 and 144 | 18000 |