Least Common Multiple (LCM) of 63 and 174
The least common multiple (LCM) of 63 and 174 is 3654.
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 63 and 174?
First, calculate the GCD of 63 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 174 = 0 remainder 63 |
| 2 | 174 ÷ 63 = 2 remainder 48 |
| 3 | 63 ÷ 48 = 1 remainder 15 |
| 4 | 48 ÷ 15 = 3 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 65 | 8970 |
| 186 and 119 | 22134 |
| 65 and 46 | 2990 |
| 90 and 177 | 5310 |
| 59 and 17 | 1003 |