Least Common Multiple (LCM) of 101 and 135
The least common multiple (LCM) of 101 and 135 is 13635.
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 135?
First, calculate the GCD of 101 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 135 = 0 remainder 101 |
| 2 | 135 ÷ 101 = 1 remainder 34 |
| 3 | 101 ÷ 34 = 2 remainder 33 |
| 4 | 34 ÷ 33 = 1 remainder 1 |
| 5 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 105 | 210 |
| 165 and 94 | 15510 |
| 27 and 93 | 837 |
| 46 and 138 | 138 |
| 171 and 139 | 23769 |