Least Common Multiple (LCM) of 174 and 72
The least common multiple (LCM) of 174 and 72 is 2088.
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 174 and 72?
First, calculate the GCD of 174 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 72 = 2 remainder 30 |
| 2 | 72 ÷ 30 = 2 remainder 12 |
| 3 | 30 ÷ 12 = 2 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 138 | 3864 |
| 69 and 72 | 1656 |
| 121 and 44 | 484 |
| 144 and 42 | 1008 |
| 89 and 128 | 11392 |