एचसीएफ 306 657 9 दिया है एलसीएम 306 657 ज्ञात कीजिए - echaseeeph 306 657 9 diya hai elaseeem 306 657 gyaat keejie

Answer

Hint: To solve the given question, we will first find out what are the full forms of LCM and HCF and what they actually are. Then, we will write the numbers 306 and 657 as the product of prime numbers. Then we will select the numbers which are common to both 306 and 657. Then we will multiply these selected numbers. The LCM of these two numbers will be a product of these selected numbers and the remaining numbers.

Complete step-by-step answer:
Before, solving the question, we must know what HCF and LCM are. HCF is the short form of the highest common factor. HCF of two or more numbers is the largest positive integer that divides each of the integers. LCM is the short form of the lowest common multiple. LCM of two or more numbers is the smallest positive integer that is divisible by each of the integers. Now, we are asked to find the LCM of 306 and 657. For this, we will do prime factorization of 306 and 657. Thus, the prime factorization of 306 is:

Note: The alternate method of finding the LCM of 306 and 657 is shown below. We know that if tow positive integers are given then their product will be equal to the product of HCF and LCM of these two integers. Thus, we can say that,
\[LCM\times HCF=\text{ product of numbers}\]
\[\Rightarrow LCM\times 9=306\times 657\]
\[\Rightarrow LCM=\dfrac{306\times 657}{9}\]
\[\Rightarrow LCM=22338\]

Solution:

We know that LCM × HCF = product of two given integers

Given, HCF (306, 657) = 9

We have to find, LCM (306, 657) 

We have the given numbers 306 and 657. Hence, we can find the product of 306 and 657. The HCF of these two numbers is 9. Substitute these values in the above formula and find the value of the unknown i.e. LCM.

LCM × 9 = 306 × 657

LCM = (306 × 657) / 9

LCM = 34 × 657

LCM = 22338

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

Video Solution:

Given that HCF (306, 657) = 9, find LCM (306, 657)

NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.2 Question 4

Summary:

Given that HCF (306, 657) = 9, the LCM (306, 657) is 22338.

☛ Related Questions:

• Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
• Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
• Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
• Check whether 6n can end with the digit 0 for any natural number n.

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asked Aug 13, 2019 in Mathematics by Rk Roy (63.9k points)

HCF (306, 657) = 9 दिया है। LCM (306, 657) ज्ञात कीजिए।

• real numbers

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1 Answer

+1 vote

answered Aug 13, 2019 by KumarManish (57.9k points)
selected Oct 12, 2019 by Vikash Kumar

Best answer

HCF (306, 657) अर्थात् 306 और 657 का HCF = 9 

चूंकि LCM x HCF = संख्याओं का गुणनफल

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