Least Common Multiple (LCM) of 74 and 113
The least common multiple (LCM) of 74 and 113 is 8362.
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 113?
First, calculate the GCD of 74 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 113 = 0 remainder 74 |
| 2 | 113 ÷ 74 = 1 remainder 39 |
| 3 | 74 ÷ 39 = 1 remainder 35 |
| 4 | 39 ÷ 35 = 1 remainder 4 |
| 5 | 35 ÷ 4 = 8 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 78 | 2496 |
| 39 and 15 | 195 |
| 46 and 190 | 4370 |
| 115 and 117 | 13455 |
| 31 and 170 | 5270 |