Least Common Multiple (LCM) of 45 and 75
The least common multiple (LCM) of 45 and 75 is 225.
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 45 and 75?
First, calculate the GCD of 45 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 75 = 0 remainder 45 |
| 2 | 75 ÷ 45 = 1 remainder 30 |
| 3 | 45 ÷ 30 = 1 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 109 | 16568 |
| 138 and 117 | 5382 |
| 125 and 99 | 12375 |
| 105 and 23 | 2415 |
| 164 and 69 | 11316 |