Least Common Multiple (LCM) of 176 and 74
The least common multiple (LCM) of 176 and 74 is 6512.
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 74?
First, calculate the GCD of 176 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 74 = 2 remainder 28 |
| 2 | 74 ÷ 28 = 2 remainder 18 |
| 3 | 28 ÷ 18 = 1 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 17 | 340 |
| 87 and 129 | 3741 |
| 105 and 101 | 10605 |
| 38 and 132 | 2508 |
| 63 and 100 | 6300 |