Least Common Multiple (LCM) of 36 and 49
The least common multiple (LCM) of 36 and 49 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 36 and 49?
First, calculate the GCD of 36 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 49 = 0 remainder 36 |
| 2 | 49 ÷ 36 = 1 remainder 13 |
| 3 | 36 ÷ 13 = 2 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 192 | 29760 |
| 59 and 149 | 8791 |
| 166 and 47 | 7802 |
| 133 and 146 | 19418 |
| 113 and 167 | 18871 |