How many multiples of both 3 or 4 are there from 1 to 100 in total?

Question: How many multiples of both 3 or 4 are there from 1 to 100 in total?Solution: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 from 1 to 100 is 50