Least Common Multiple (LCM) of 106 and 176
The least common multiple (LCM) of 106 and 176 is 9328.
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 176?
First, calculate the GCD of 106 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 176 = 0 remainder 106 |
| 2 | 176 ÷ 106 = 1 remainder 70 |
| 3 | 106 ÷ 70 = 1 remainder 36 |
| 4 | 70 ÷ 36 = 1 remainder 34 |
| 5 | 36 ÷ 34 = 1 remainder 2 |
| 6 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 90 | 1530 |
| 36 and 64 | 576 |
| 18 and 146 | 1314 |
| 160 and 184 | 3680 |
| 31 and 127 | 3937 |