Least Common Multiple (LCM) of 69 and 177
The least common multiple (LCM) of 69 and 177 is 4071.
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 177?
First, calculate the GCD of 69 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 177 = 0 remainder 69 |
| 2 | 177 ÷ 69 = 2 remainder 39 |
| 3 | 69 ÷ 39 = 1 remainder 30 |
| 4 | 39 ÷ 30 = 1 remainder 9 |
| 5 | 30 ÷ 9 = 3 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 90 | 1170 |
| 144 and 75 | 3600 |
| 194 and 164 | 15908 |
| 82 and 157 | 12874 |
| 102 and 143 | 14586 |