Least Common Multiple (LCM) of 100 and 144
The least common multiple (LCM) of 100 and 144 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 100 and 144?
First, calculate the GCD of 100 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 144 = 0 remainder 100 |
| 2 | 144 ÷ 100 = 1 remainder 44 |
| 3 | 100 ÷ 44 = 2 remainder 12 |
| 4 | 44 ÷ 12 = 3 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 156 | 30732 |
| 157 and 197 | 30929 |
| 60 and 81 | 1620 |
| 175 and 87 | 15225 |
| 43 and 183 | 7869 |