Least Common Multiple (LCM) of 34 and 74
The least common multiple (LCM) of 34 and 74 is 1258.
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 34 and 74?
First, calculate the GCD of 34 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 74 = 0 remainder 34 |
| 2 | 74 ÷ 34 = 2 remainder 6 |
| 3 | 34 ÷ 6 = 5 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 184 | 8280 |
| 10 and 115 | 230 |
| 72 and 184 | 1656 |
| 119 and 127 | 15113 |
| 24 and 24 | 24 |