Least Common Multiple (LCM) of 37 and 144
The least common multiple (LCM) of 37 and 144 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 37 and 144?
First, calculate the GCD of 37 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 144 = 0 remainder 37 |
| 2 | 144 ÷ 37 = 3 remainder 33 |
| 3 | 37 ÷ 33 = 1 remainder 4 |
| 4 | 33 ÷ 4 = 8 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 86 | 14362 |
| 121 and 49 | 5929 |
| 183 and 90 | 5490 |
| 32 and 38 | 608 |
| 170 and 65 | 2210 |