Least Common Multiple (LCM) of 101 and 17
The least common multiple (LCM) of 101 and 17 is 1717.
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 17?
First, calculate the GCD of 101 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 17 = 5 remainder 16 |
| 2 | 17 ÷ 16 = 1 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 49 | 784 |
| 134 and 38 | 2546 |
| 73 and 18 | 1314 |
| 103 and 34 | 3502 |
| 174 and 11 | 1914 |