Least Common Multiple (LCM) of 53 and 21
The least common multiple (LCM) of 53 and 21 is 1113.
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 53 and 21?
First, calculate the GCD of 53 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 21 = 2 remainder 11 |
| 2 | 21 ÷ 11 = 1 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 106 | 1590 |
| 104 and 86 | 4472 |
| 50 and 16 | 400 |
| 113 and 37 | 4181 |
| 173 and 98 | 16954 |