Least Common Multiple (LCM) of 106 and 17
The least common multiple (LCM) of 106 and 17 is 1802.
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 106 and 17?
First, calculate the GCD of 106 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 17 = 6 remainder 4 |
| 2 | 17 ÷ 4 = 4 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 40 | 760 |
| 63 and 50 | 3150 |
| 114 and 135 | 5130 |
| 57 and 137 | 7809 |
| 20 and 118 | 1180 |