Least Common Multiple (LCM) of 65 and 114
The least common multiple (LCM) of 65 and 114 is 7410.
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 114?
First, calculate the GCD of 65 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 114 = 0 remainder 65 |
| 2 | 114 ÷ 65 = 1 remainder 49 |
| 3 | 65 ÷ 49 = 1 remainder 16 |
| 4 | 49 ÷ 16 = 3 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 148 | 13468 |
| 48 and 100 | 1200 |
| 65 and 102 | 6630 |
| 137 and 126 | 17262 |
| 32 and 112 | 224 |