Least Common Multiple (LCM) of 123 and 136
The least common multiple (LCM) of 123 and 136 is 16728.
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 136?
First, calculate the GCD of 123 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 136 = 0 remainder 123 |
| 2 | 136 ÷ 123 = 1 remainder 13 |
| 3 | 123 ÷ 13 = 9 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 53 | 3869 |
| 162 and 105 | 5670 |
| 75 and 140 | 2100 |
| 47 and 117 | 5499 |
| 20 and 14 | 140 |