Least Common Multiple (LCM) of 60 and 153
The least common multiple (LCM) of 60 and 153 is 3060.
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 60 and 153?
First, calculate the GCD of 60 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 153 = 0 remainder 60 |
| 2 | 153 ÷ 60 = 2 remainder 33 |
| 3 | 60 ÷ 33 = 1 remainder 27 |
| 4 | 33 ÷ 27 = 1 remainder 6 |
| 5 | 27 ÷ 6 = 4 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 100 | 2900 |
| 134 and 13 | 1742 |
| 60 and 68 | 1020 |
| 134 and 118 | 7906 |
| 112 and 160 | 1120 |