Least Common Multiple (LCM) of 72 and 176
The least common multiple (LCM) of 72 and 176 is 1584.
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 72 and 176?
First, calculate the GCD of 72 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 176 = 0 remainder 72 |
| 2 | 176 ÷ 72 = 2 remainder 32 |
| 3 | 72 ÷ 32 = 2 remainder 8 |
| 4 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 40 | 840 |
| 99 and 65 | 6435 |
| 44 and 28 | 308 |
| 126 and 115 | 14490 |
| 152 and 102 | 7752 |