Least Common Multiple (LCM) of 65 and 90
The least common multiple (LCM) of 65 and 90 is 1170.
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 90?
First, calculate the GCD of 65 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 90 = 0 remainder 65 |
| 2 | 90 ÷ 65 = 1 remainder 25 |
| 3 | 65 ÷ 25 = 2 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 102 | 7854 |
| 34 and 156 | 2652 |
| 68 and 191 | 12988 |
| 14 and 110 | 770 |
| 91 and 78 | 546 |