#
There are certain number of positive integers, which are

multiple of 15 and lie between 100 and 1 Lakh Of these how

many are multiple of 35

## Answers

**Answer:**

there are ten

**Step-by-step explanation:**

35,70,105,140,175,210,245,280,315,350

**Answer:**

**The number of multiples of 15 between 100 and 1 lakh, which are also multiple of 35 = 952**

**Step-by-step explanation:**

**To find,**

The number positive integers which are multiples both 15 and 35 between 100 and 1 lakh

**Recall the formula**

**The number of terms in an AP **

**n = ****, -----------------(1) **

**where tₙ is the last term and t₁ is the first term and d is the common difference of the AP**

**Solution:**

__To find LCM(15,35)__

Prime factorization of 15 = 3×5

Prime factorization of 35 = 5×7

**LCM of 15 and 35 = 3×5×7 = 105**

Hence multiples of 15 which are also multiples of 35 are the multiples of 105

Now, we need to calculate the number of multiples of 105 between 100 and 1 lakh

**The first multiple of 105 between 100 and 1lakh = 105**

__To find the last multiple of 105 between 100 and 1lakh__

On dividing 1 lakh by 105, we get

quotient = 952 and remainder = 40

Then we can write,

100000 = 952×105 + 40

100000 - 40 = 952×105, a multiple of 105

**Hence the last multiple of 105, between 100 and 1 lakh = 99960**

The multiples of 105 between 100 and 1lakh are

**105,210,315,..............., 99960**

**This sequence forms an AP and is required to find the number of terms in this AP**

Here first term t₁ = 105

last term tₙ = 99960

common difference =d = 105

Then from equation (1),** the number of terms of the AP = **

=

= 951 +1

= 952

∴** The number of multiples of 15 between 100 and 1 lakh, which are also multiple of 35 = 952**

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