Least Common Multiple (LCM) of 65 and 36
The least common multiple (LCM) of 65 and 36 is 2340.
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 36?
First, calculate the GCD of 65 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 36 = 1 remainder 29 |
| 2 | 36 ÷ 29 = 1 remainder 7 |
| 3 | 29 ÷ 7 = 4 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 23 | 2369 |
| 90 and 162 | 810 |
| 112 and 115 | 12880 |
| 157 and 30 | 4710 |
| 160 and 140 | 1120 |