Least Common Multiple (LCM) of 123 and 152
The least common multiple (LCM) of 123 and 152 is 18696.
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 152?
First, calculate the GCD of 123 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 152 = 0 remainder 123 |
| 2 | 152 ÷ 123 = 1 remainder 29 |
| 3 | 123 ÷ 29 = 4 remainder 7 |
| 4 | 29 ÷ 7 = 4 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 56 | 6216 |
| 164 and 30 | 2460 |
| 14 and 198 | 1386 |
| 78 and 130 | 390 |
| 100 and 114 | 5700 |