Question
Download Solution PDFHow many multiples of both 3 or 4 are there from 1 to 100 in total?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
n(A∪B) = n(A) + n(B) - n(A∩B)
Calculation:
On dividing 100 by 3 we get a quotient of 33
The number of multiple of 3, n(A) = 33
On dividing 100 by 4 we get a quotient of 25
The number of multiple of 4, n(B) = 25
LCM of 3 and 4 is 12
On dividing 100 by 12 we get a quotient of 8
The number of multiple of 12, n(A∩B) = 8
The number which is multiple of 3 or 4 = n(A∪B)
Now, n(A∪B) = n(A) + n(B) - n(A∩B)
⇒ 33 + 25 - 8
⇒ 50
∴ The total number multiple of 3 or 4 is 50
Last updated on Jul 14, 2025
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