Least Common Multiple (LCM) of 49 and 72
The least common multiple (LCM) of 49 and 72 is 3528.
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 49 and 72?
First, calculate the GCD of 49 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 72 = 0 remainder 49 |
| 2 | 72 ÷ 49 = 1 remainder 23 |
| 3 | 49 ÷ 23 = 2 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 176 | 19536 |
| 66 and 102 | 1122 |
| 130 and 55 | 1430 |
| 174 and 84 | 2436 |
| 144 and 54 | 432 |