Least Common Multiple (LCM) of 72 and 49
The least common multiple (LCM) of 72 and 49 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 72 and 49?
First, calculate the GCD of 72 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 49 = 1 remainder 23 |
| 2 | 49 ÷ 23 = 2 remainder 3 |
| 3 | 23 ÷ 3 = 7 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 102 | 9588 |
| 110 and 62 | 3410 |
| 68 and 16 | 272 |
| 49 and 106 | 5194 |
| 103 and 76 | 7828 |