Least Common Multiple (LCM) of 49 and 69
The least common multiple (LCM) of 49 and 69 is 3381.
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 49 and 69?
First, calculate the GCD of 49 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 69 = 0 remainder 49 |
| 2 | 69 ÷ 49 = 1 remainder 20 |
| 3 | 49 ÷ 20 = 2 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 195 | 390 |
| 179 and 86 | 15394 |
| 108 and 115 | 12420 |
| 95 and 69 | 6555 |
| 141 and 102 | 4794 |