Least Common Multiple (LCM) of 69 and 74
The least common multiple (LCM) of 69 and 74 is 5106.
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 69 and 74?
First, calculate the GCD of 69 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 74 = 0 remainder 69 |
| 2 | 74 ÷ 69 = 1 remainder 5 |
| 3 | 69 ÷ 5 = 13 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 54 | 702 |
| 132 and 133 | 17556 |
| 106 and 78 | 4134 |
| 169 and 49 | 8281 |
| 174 and 157 | 27318 |