Least Common Multiple (LCM) of 101 and 75
The least common multiple (LCM) of 101 and 75 is 7575.
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 101 and 75?
First, calculate the GCD of 101 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 75 = 1 remainder 26 |
| 2 | 75 ÷ 26 = 2 remainder 23 |
| 3 | 26 ÷ 23 = 1 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 163 | 15648 |
| 119 and 20 | 2380 |
| 18 and 69 | 414 |
| 197 and 192 | 37824 |
| 31 and 135 | 4185 |