Least Common Multiple (LCM) of 27 and 91
The least common multiple (LCM) of 27 and 91 is 2457.
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 91?
First, calculate the GCD of 27 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 91 = 0 remainder 27 |
| 2 | 91 ÷ 27 = 3 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 |
|---|---|
| 118 and 40 | 2360 |
| 124 and 13 | 1612 |
| 13 and 10 | 130 |
| 43 and 184 | 7912 |
| 179 and 187 | 33473 |