Least Common Multiple (LCM) of 101 and 27
The least common multiple (LCM) of 101 and 27 is 2727.
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 101 and 27?
First, calculate the GCD of 101 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 27 = 3 remainder 20 |
| 2 | 27 ÷ 20 = 1 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 11 | 1199 |
| 135 and 82 | 11070 |
| 124 and 113 | 14012 |
| 187 and 175 | 32725 |
| 149 and 170 | 25330 |