Least Common Multiple (LCM) of 69 and 176
The least common multiple (LCM) of 69 and 176 is 12144.
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 69 and 176?
First, calculate the GCD of 69 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 176 = 0 remainder 69 |
| 2 | 176 ÷ 69 = 2 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 |
|---|---|
| 81 and 80 | 6480 |
| 89 and 46 | 4094 |
| 159 and 36 | 1908 |
| 100 and 162 | 8100 |
| 191 and 173 | 33043 |