Friday

July 25, 2014

July 25, 2014

Posted by **Debbie** on Thursday, October 25, 2012 at 7:14pm.

- math -
**Reiny**, Thursday, October 25, 2012 at 7:28pmto be multiples of 4 and 6, they must be multiples of 12, the LCM

The smallest 3-digit multiple of 12 is

108 , then 120 , 132 .. .996

consider this to be an arithmetic sequence

a = 108, d = 12 , n = ? -- the number of terms

t(n) = a + (n-1)d

996 = 108 + 12(n-1)

888 = 12n - 24

12n = 912

n = 76

There are 76 of them

- math -
**Debbie**, Friday, October 26, 2012 at 7:26pmSince 12n = 12(5m+1)= 60m +12, our goal is to now count integers m such that 100 less than or equal to 60m +12<1000. Subtracing 12 from each part of the inequality, we get 88 lees than or equal to 60m<988. Dividing by 60, we get 2 less than or equal to m less than or equal to 16, so there are 16-1=15 values for the integer m that give us the three-digit multiples of 4 and 6 that have units digits of 2.

**Related Questions**

math - There are 900 three-digit integers. The number of three-digit integers ...

Math - There are 900 three-digit integers. The number of three-digit integers ...

Math - How many positive three-digit integers have the property that the tens ...

Math (Combinatorics) - How many 4 digit positive integers have the ones digit a ...

math - my thousand digit is half my ones digit.my houndreds digit is odd and ...

math - The number uses every number 0-9 the numbers are used only once the ...

Mathe - The number has two digits. Both of the digits are even.the digit in the ...

math - i am a three digit number. my hundreds digit is three more than my ones ...

Mathematics - how many positive four- digit integers have 3 as their tens digit ...

math - i have a six digit question my 100 thousands is one less than my ones ...