Least Common Multiple (LCM) of 53 and 153
The least common multiple (LCM) of 53 and 153 is 8109.
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 153?
First, calculate the GCD of 53 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 153 = 0 remainder 53 |
| 2 | 153 ÷ 53 = 2 remainder 47 |
| 3 | 53 ÷ 47 = 1 remainder 6 |
| 4 | 47 ÷ 6 = 7 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 100 | 5300 |
| 160 and 24 | 480 |
| 88 and 186 | 8184 |
| 76 and 52 | 988 |
| 85 and 16 | 1360 |