Least Common Multiple (LCM) of 123 and 88
The least common multiple (LCM) of 123 and 88 is 10824.
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 88?
First, calculate the GCD of 123 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 88 = 1 remainder 35 |
| 2 | 88 ÷ 35 = 2 remainder 18 |
| 3 | 35 ÷ 18 = 1 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 197 | 8865 |
| 96 and 120 | 480 |
| 14 and 20 | 140 |
| 143 and 64 | 9152 |
| 151 and 17 | 2567 |