Least Common Multiple (LCM) of 61 and 75
The least common multiple (LCM) of 61 and 75 is 4575.
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 75?
First, calculate the GCD of 61 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 75 = 0 remainder 61 |
| 2 | 75 ÷ 61 = 1 remainder 14 |
| 3 | 61 ÷ 14 = 4 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 165 | 1320 |
| 101 and 191 | 19291 |
| 134 and 68 | 4556 |
| 170 and 48 | 4080 |
| 17 and 187 | 187 |