Least Common Multiple (LCM) of 126 and 174
The least common multiple (LCM) of 126 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 126 and 174?
First, calculate the GCD of 126 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 174 = 0 remainder 126 |
| 2 | 174 ÷ 126 = 1 remainder 48 |
| 3 | 126 ÷ 48 = 2 remainder 30 |
| 4 | 48 ÷ 30 = 1 remainder 18 |
| 5 | 30 ÷ 18 = 1 remainder 12 |
| 6 | 18 ÷ 12 = 1 remainder 6 |
| 7 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 169 | 16731 |
| 72 and 32 | 288 |
| 38 and 99 | 3762 |
| 98 and 150 | 7350 |
| 172 and 82 | 7052 |