Least Common Multiple (LCM) of 144 and 100
The least common multiple (LCM) of 144 and 100 is 3600.
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 100?
First, calculate the GCD of 144 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 100 = 1 remainder 44 |
| 2 | 100 ÷ 44 = 2 remainder 12 |
| 3 | 44 ÷ 12 = 3 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 150 | 5100 |
| 65 and 108 | 7020 |
| 46 and 135 | 6210 |
| 191 and 41 | 7831 |
| 67 and 120 | 8040 |