Least Common Multiple (LCM) of 27 and 97
The least common multiple (LCM) of 27 and 97 is 2619.
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 97?
First, calculate the GCD of 27 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 97 = 0 remainder 27 |
| 2 | 97 ÷ 27 = 3 remainder 16 |
| 3 | 27 ÷ 16 = 1 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 38 | 3040 |
| 169 and 115 | 19435 |
| 71 and 160 | 11360 |
| 152 and 66 | 5016 |
| 20 and 153 | 3060 |