Least Common Multiple (LCM) of 144 and 74
The least common multiple (LCM) of 144 and 74 is 5328.
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 144 and 74?
First, calculate the GCD of 144 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 74 = 1 remainder 70 |
| 2 | 74 ÷ 70 = 1 remainder 4 |
| 3 | 70 ÷ 4 = 17 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 146 | 2628 |
| 16 and 40 | 80 |
| 148 and 162 | 11988 |
| 60 and 109 | 6540 |
| 113 and 35 | 3955 |