Least Common Multiple (LCM) of 75 and 101
The least common multiple (LCM) of 75 and 101 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 75 and 101?
First, calculate the GCD of 75 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 101 = 0 remainder 75 |
| 2 | 101 ÷ 75 = 1 remainder 26 |
| 3 | 75 ÷ 26 = 2 remainder 23 |
| 4 | 26 ÷ 23 = 1 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 63 | 7245 |
| 191 and 56 | 10696 |
| 167 and 54 | 9018 |
| 70 and 19 | 1330 |
| 77 and 178 | 13706 |