Least Common Multiple (LCM) of 44 and 67
The least common multiple (LCM) of 44 and 67 is 2948.
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 67?
First, calculate the GCD of 44 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 67 = 0 remainder 44 |
| 2 | 67 ÷ 44 = 1 remainder 23 |
| 3 | 44 ÷ 23 = 1 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 36 | 2556 |
| 106 and 190 | 10070 |
| 130 and 156 | 780 |
| 104 and 83 | 8632 |
| 71 and 44 | 3124 |