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 |
|---|---|
| 87 and 198 | 5742 |
| 189 and 113 | 21357 |
| 153 and 134 | 20502 |
| 110 and 141 | 15510 |
| 129 and 28 | 3612 |