Least Common Multiple (LCM) of 27 and 37
The least common multiple (LCM) of 27 and 37 is 999.
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 27 and 37?
First, calculate the GCD of 27 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 37 = 0 remainder 27 |
| 2 | 37 ÷ 27 = 1 remainder 10 |
| 3 | 27 ÷ 10 = 2 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 35 | 1995 |
| 64 and 32 | 64 |
| 172 and 68 | 2924 |
| 150 and 109 | 16350 |
| 103 and 154 | 15862 |