Least Common Multiple (LCM) of 65 and 75
The least common multiple (LCM) of 65 and 75 is 975.
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 65 and 75?
First, calculate the GCD of 65 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 75 = 0 remainder 65 |
| 2 | 75 ÷ 65 = 1 remainder 10 |
| 3 | 65 ÷ 10 = 6 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 112 | 672 |
| 169 and 101 | 17069 |
| 61 and 167 | 10187 |
| 199 and 73 | 14527 |
| 46 and 171 | 7866 |