Least Common Multiple (LCM) of 64 and 123
The least common multiple (LCM) of 64 and 123 is 7872.
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 64 and 123?
First, calculate the GCD of 64 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 123 = 0 remainder 64 |
| 2 | 123 ÷ 64 = 1 remainder 59 |
| 3 | 64 ÷ 59 = 1 remainder 5 |
| 4 | 59 ÷ 5 = 11 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 181 | 24978 |
| 98 and 78 | 3822 |
| 101 and 119 | 12019 |
| 82 and 110 | 4510 |
| 154 and 30 | 2310 |