Least Common Multiple (LCM) of 176 and 107
The least common multiple (LCM) of 176 and 107 is 18832.
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 176 and 107?
First, calculate the GCD of 176 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 107 = 1 remainder 69 |
| 2 | 107 ÷ 69 = 1 remainder 38 |
| 3 | 69 ÷ 38 = 1 remainder 31 |
| 4 | 38 ÷ 31 = 1 remainder 7 |
| 5 | 31 ÷ 7 = 4 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 75 | 2775 |
| 110 and 94 | 5170 |
| 120 and 157 | 18840 |
| 81 and 21 | 567 |
| 150 and 99 | 4950 |