Least Common Multiple (LCM) of 36 and 144
The least common multiple (LCM) of 36 and 144 is 144.
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 36 and 144?
First, calculate the GCD of 36 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 144 = 0 remainder 36 |
| 2 | 144 ÷ 36 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 106 | 9328 |
| 164 and 77 | 12628 |
| 190 and 121 | 22990 |
| 101 and 57 | 5757 |
| 103 and 27 | 2781 |