Least Common Multiple (LCM) of 65 and 152
The least common multiple (LCM) of 65 and 152 is 9880.
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 152?
First, calculate the GCD of 65 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 152 = 0 remainder 65 |
| 2 | 152 ÷ 65 = 2 remainder 22 |
| 3 | 65 ÷ 22 = 2 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 76 | 14212 |
| 131 and 30 | 3930 |
| 128 and 28 | 896 |
| 152 and 23 | 3496 |
| 200 and 60 | 600 |