Least Common Multiple (LCM) of 32 and 49
The least common multiple (LCM) of 32 and 49 is 1568.
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 32 and 49?
First, calculate the GCD of 32 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 49 = 0 remainder 32 |
| 2 | 49 ÷ 32 = 1 remainder 17 |
| 3 | 32 ÷ 17 = 1 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 13 | 1170 |
| 124 and 110 | 6820 |
| 179 and 110 | 19690 |
| 143 and 28 | 4004 |
| 144 and 157 | 22608 |