Least Common Multiple (LCM) of 132 and 174
The least common multiple (LCM) of 132 and 174 is 3828.
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 132 and 174?
First, calculate the GCD of 132 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 174 = 0 remainder 132 |
| 2 | 174 ÷ 132 = 1 remainder 42 |
| 3 | 132 ÷ 42 = 3 remainder 6 |
| 4 | 42 ÷ 6 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 81 | 12312 |
| 161 and 103 | 16583 |
| 152 and 188 | 7144 |
| 157 and 89 | 13973 |
| 110 and 80 | 880 |