Least Common Multiple (LCM) of 38 and 53
The least common multiple (LCM) of 38 and 53 is 2014.
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 38 and 53?
First, calculate the GCD of 38 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 53 = 0 remainder 38 |
| 2 | 53 ÷ 38 = 1 remainder 15 |
| 3 | 38 ÷ 15 = 2 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 160 | 10720 |
| 184 and 124 | 5704 |
| 23 and 157 | 3611 |
| 191 and 136 | 25976 |
| 198 and 156 | 5148 |