Least Common Multiple (LCM) of 117 and 74
The least common multiple (LCM) of 117 and 74 is 8658.
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 117 and 74?
First, calculate the GCD of 117 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 74 = 1 remainder 43 |
| 2 | 74 ÷ 43 = 1 remainder 31 |
| 3 | 43 ÷ 31 = 1 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 146 | 22630 |
| 120 and 39 | 1560 |
| 47 and 116 | 5452 |
| 16 and 27 | 432 |
| 90 and 150 | 450 |