The Least Multiple of 7 which Leaves a Remainder of 4, when Divided by 6, 9, 15 and 18 is?

Least Multiple of 7 Leaving Remainder of 4

364 is the least multiple of 7 which when divided by 6, 9, 15, and 18 leaves a remainder 4. To prove this, we will first find the LCM of 6, 9, 15, and 18. For this, we will use the prime factorization method which works by finding out the factors of numbers.

The L.C.M of 6, 9, 15, and 18 is 90.

Now, as we are aware that our remainder is 4, we will add 4 to the LCM we have derived in the statement above.

90 + 4 = 94

As 94 is not divisible by 7, we will use the next multiple of 90 which is 180. We will again add 4 to it which will give us the value 184.

180 + 4 = 184

again, 184 is not divisible by 7. Hence, we will consider the next multiple of 90 which is 270, and repeat the same process.

270 + 4 = 274

274 is also not divisible by 7 so, now we will take the next multiple of 90 which is 360.

360 + 4 = 364

364 is divisible by 7 as,

364/7 = 52

Hence, the least multiple of 7 which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is 364.

What are Multiples?

A multiple is a mathematical term that refers to the number we get when two other numbers are multiplied. We get multiples when two whole numbers are multiplied by each other. Every number is multiple in itself. Another important thing to note is that a number can have infinite multiples. Except for 0, all multiples of a number are either equal to it or greater than it.

Many confuse multiples with factors, however, they are different. The major difference between factor and multiple is that factor refers to the number which can divide a number completely leaving zero as a remainder.

Summary:

The Least Multiple of 7 which Leaves a Remainder of 4, when Divided by 6, 9, 15 and 18 is?

364 is the least multiple of 7 which leaves a remainder of 4, when divided by 6, 9, 15 and 18. We derived this answer by finding out the LCM of divisors and then checking multiples of the LCM to know whether they are divisible by 7 or not. 

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