Least Common Multiple (LCM) of 49 and 177
The least common multiple (LCM) of 49 and 177 is 8673.
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 49 and 177?
First, calculate the GCD of 49 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 177 = 0 remainder 49 |
| 2 | 177 ÷ 49 = 3 remainder 30 |
| 3 | 49 ÷ 30 = 1 remainder 19 |
| 4 | 30 ÷ 19 = 1 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 99 | 15840 |
| 100 and 129 | 12900 |
| 83 and 100 | 8300 |
| 63 and 106 | 6678 |
| 167 and 63 | 10521 |