Least Common Multiple (LCM) of 49 and 119
The least common multiple (LCM) of 49 and 119 is 833.
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 119?
First, calculate the GCD of 49 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 119 = 0 remainder 49 |
| 2 | 119 ÷ 49 = 2 remainder 21 |
| 3 | 49 ÷ 21 = 2 remainder 7 |
| 4 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 51 | 5610 |
| 50 and 55 | 550 |
| 11 and 150 | 1650 |
| 109 and 41 | 4469 |
| 105 and 143 | 15015 |