Least Common Multiple (LCM) of 123 and 65
The least common multiple (LCM) of 123 and 65 is 7995.
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 123 and 65?
First, calculate the GCD of 123 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 65 = 1 remainder 58 |
| 2 | 65 ÷ 58 = 1 remainder 7 |
| 3 | 58 ÷ 7 = 8 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 106 | 742 |
| 105 and 151 | 15855 |
| 39 and 169 | 507 |
| 157 and 80 | 12560 |
| 101 and 42 | 4242 |