Least Common Multiple (LCM) of 74 and 123
The least common multiple (LCM) of 74 and 123 is 9102.
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 74 and 123?
First, calculate the GCD of 74 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 123 = 0 remainder 74 |
| 2 | 123 ÷ 74 = 1 remainder 49 |
| 3 | 74 ÷ 49 = 1 remainder 25 |
| 4 | 49 ÷ 25 = 1 remainder 24 |
| 5 | 25 ÷ 24 = 1 remainder 1 |
| 6 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 144 | 5904 |
| 149 and 109 | 16241 |
| 35 and 27 | 945 |
| 113 and 135 | 15255 |
| 118 and 117 | 13806 |