Least Common Multiple (LCM) of 61 and 123
The least common multiple (LCM) of 61 and 123 is 7503.
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 61 and 123?
First, calculate the GCD of 61 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 123 = 0 remainder 61 |
| 2 | 123 ÷ 61 = 2 remainder 1 |
| 3 | 61 ÷ 1 = 61 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 195 | 1365 |
| 174 and 111 | 6438 |
| 163 and 81 | 13203 |
| 28 and 32 | 224 |
| 145 and 30 | 870 |