Least Common Multiple (LCM) of 49 and 36
The least common multiple (LCM) of 49 and 36 is 1764.
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 36?
First, calculate the GCD of 49 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 36 = 1 remainder 13 |
| 2 | 36 ÷ 13 = 2 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 160 | 3040 |
| 128 and 167 | 21376 |
| 120 and 100 | 600 |
| 50 and 38 | 950 |
| 175 and 164 | 28700 |