Least Common Multiple (LCM) of 109 and 49
The least common multiple (LCM) of 109 and 49 is 5341.
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 109 and 49?
First, calculate the GCD of 109 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 49 = 2 remainder 11 |
| 2 | 49 ÷ 11 = 4 remainder 5 |
| 3 | 11 ÷ 5 = 2 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 40 | 7160 |
| 53 and 128 | 6784 |
| 71 and 153 | 10863 |
| 73 and 47 | 3431 |
| 141 and 106 | 14946 |