Least Common Multiple (LCM) of 74 and 117
The least common multiple (LCM) of 74 and 117 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 74 and 117?
First, calculate the GCD of 74 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 117 = 0 remainder 74 |
| 2 | 117 ÷ 74 = 1 remainder 43 |
| 3 | 74 ÷ 43 = 1 remainder 31 |
| 4 | 43 ÷ 31 = 1 remainder 12 |
| 5 | 31 ÷ 12 = 2 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 65 | 12805 |
| 106 and 99 | 10494 |
| 98 and 83 | 8134 |
| 92 and 112 | 2576 |
| 61 and 141 | 8601 |