Least Common Multiple (LCM) of 172 and 106
The least common multiple (LCM) of 172 and 106 is 9116.
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 172 and 106?
First, calculate the GCD of 172 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 106 = 1 remainder 66 |
| 2 | 106 ÷ 66 = 1 remainder 40 |
| 3 | 66 ÷ 40 = 1 remainder 26 |
| 4 | 40 ÷ 26 = 1 remainder 14 |
| 5 | 26 ÷ 14 = 1 remainder 12 |
| 6 | 14 ÷ 12 = 1 remainder 2 |
| 7 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 47 | 6862 |
| 100 and 74 | 3700 |
| 104 and 70 | 3640 |
| 151 and 103 | 15553 |
| 96 and 179 | 17184 |