Find the LCM of 2,3,5 starting from 1 to 20
Mathematics
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Step-by-step solution
5 stepsList the multiples of each number up to 20.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Multiples of 3: 3, 6, 9, 12, 15, 18
Multiples of 5: 5, 10, 15, 20Identify common multiples.
Common multiples of 2 and 3: 6, 12, 18
Common multiples of 2 and 5: 10, 20
Common multiples of 3 and 5: 15Find the smallest number that appears in all three lists of multiples.
Looking at the multiples of 2, 3, and 5, there are no common multiples within the range of 1 to 20.
Calculate the LCM using prime factorization (since there are no common multiples in the given range).
Prime factorization of 2: 2
Prime factorization of 3: 3
Prime factorization of 5: 5
The LCM is the product of the highest powers of all prime factors that appear in any of the numbers.
LCM = 2 × 3 × 5Calculate the final LCM.
LCM = 30
The LCM of 2, 3, and 5 is 30.
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