Least Common Multiple (LCM) of 123 and 72
The least common multiple (LCM) of 123 and 72 is 2952.
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 72?
First, calculate the GCD of 123 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 72 = 1 remainder 51 |
| 2 | 72 ÷ 51 = 1 remainder 21 |
| 3 | 51 ÷ 21 = 2 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 17 | 1717 |
| 14 and 157 | 2198 |
| 70 and 151 | 10570 |
| 57 and 139 | 7923 |
| 89 and 128 | 11392 |