Q: Find sum of all natural numbers less than 100 and divisible by 6?

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8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

Sir, could you explain how to find it?

The numbers that are divisible by both 3 and 5 have to be a factor of 15. That leaves 15, 30, 45, 60, 75, and 90. There are 6 numbers less than 100 divisible by 3 and 5

55,50,45,40,35,30,25,20,15,10,5

There are 8 odd numbers less than 50 that are divisible by 3 They are 3, 9, 15, 21, 27, 33, 39, and 45.

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50

8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

85

2520

How many numbers less than 700 are divisible by both 15 and 21?

The natural numbers are the counting numbers. Therefore, the natural numbers less than 31 are the numbers from 1 to 30.

Sir, could you explain how to find it?

There are 9 natural numbers less than 10.

The numbers that are divisible by both 3 and 5 have to be a factor of 15. That leaves 15, 30, 45, 60, 75, and 90. There are 6 numbers less than 100 divisible by 3 and 5

55,50,45,40,35,30,25,20,15,10,5

4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100 ............ on and on and on to infinity and beyond LOL !!!!!!!!!

There aren't any odd numbers divisible by 4, much less consecutive ones.