Question

Find the hcf and lcm of 26676 and 337554 using fundamental theorem of arthmetic. Please answer me with explaination.

Answer 1

LCM = 87,76,404 and

HCF = 1026

Answer 2

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.

The highest common factor (HCF) is found by finding all common factors of two numbers and selecting the largest one. For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.

In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.

Euclid's division lemma :

Let a and b be any two positive Integers.

Then there exist two unique whole numbers q and r such that
$a=bq+r$

$0\leq r < b$

Now ,

start with a larger integer, that is 337554,

Apply the division lemma to 337554 and 26676,

$337554=26676\times12+17442$

$26676=17442\times 1+9234$

$17442=9234\times 1+8208$

$9234=8208\times 1+1026$

$8208=1026\times 8+0$

The remainder has now become zero, so our procedure stops.

Since the divisor at this stage is 1026 .

$\therefore HCF(337554,26676)=1026$

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