Least Common Multiple (LCM) of 44 and 119
The least common multiple (LCM) of 44 and 119 is 5236.
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 44 and 119?
First, calculate the GCD of 44 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 119 = 0 remainder 44 |
| 2 | 119 ÷ 44 = 2 remainder 31 |
| 3 | 44 ÷ 31 = 1 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 69 | 2622 |
| 32 and 84 | 672 |
| 174 and 139 | 24186 |
| 200 and 77 | 15400 |
| 152 and 42 | 3192 |