Least Common Multiple (LCM) of 100 and 75
The least common multiple (LCM) of 100 and 75 is 300.
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 100 and 75?
First, calculate the GCD of 100 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 75 = 1 remainder 25 |
| 2 | 75 ÷ 25 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 115 | 805 |
| 119 and 130 | 15470 |
| 61 and 168 | 10248 |
| 122 and 55 | 6710 |
| 170 and 118 | 10030 |