Least Common Multiple (LCM) of 53 and 120
The least common multiple (LCM) of 53 and 120 is 6360.
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 120?
First, calculate the GCD of 53 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 120 = 0 remainder 53 |
| 2 | 120 ÷ 53 = 2 remainder 14 |
| 3 | 53 ÷ 14 = 3 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 159 | 6519 |
| 75 and 101 | 7575 |
| 124 and 79 | 9796 |
| 90 and 41 | 3690 |
| 104 and 138 | 7176 |