Least Common Multiple (LCM) of 49 and 76
The least common multiple (LCM) of 49 and 76 is 3724.
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 76?
First, calculate the GCD of 49 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 76 = 0 remainder 49 |
| 2 | 76 ÷ 49 = 1 remainder 27 |
| 3 | 49 ÷ 27 = 1 remainder 22 |
| 4 | 27 ÷ 22 = 1 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 86 | 2150 |
| 192 and 12 | 192 |
| 52 and 53 | 2756 |
| 117 and 160 | 18720 |
| 133 and 176 | 23408 |