Least Common Multiple (LCM) of 66 and 123
The least common multiple (LCM) of 66 and 123 is 2706.
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 66 and 123?
First, calculate the GCD of 66 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 123 = 0 remainder 66 |
| 2 | 123 ÷ 66 = 1 remainder 57 |
| 3 | 66 ÷ 57 = 1 remainder 9 |
| 4 | 57 ÷ 9 = 6 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 50 | 3450 |
| 87 and 160 | 13920 |
| 123 and 198 | 8118 |
| 14 and 108 | 756 |
| 143 and 103 | 14729 |