The LCM and HCF of 36 and 288 by prime factorisation method are ..........................and ...................... respectively.
Answers
Answer:
Least Common Multiple (LCM)
The least or smallest common multiple of any two or more given natural numbers are termed as LCM. It is also termed as Lowest Common Multiple.
For example, LCM of 10, 15, and 20 is 60.
Highest Common Factor (HCF)
The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. It is also known as GCD (Greatest Common Divisor).
For example, HCF of 4, 6 and 8 is 2.
How to Find LCM and HCF?
We can find HCF and LCM of given natural numbers by two methods i.e. by prime factorization method or alternatively by division method. In the prime factorization method, given numbers are written as the product of prime factors. While in the division method, given numbers are divided by the least common factor and continue still remainder is zero.
Note: Prime numbers are numbers which have only two factors i.e. one and the number itself)
LCM by Prime Factorization Method
Here given natural numbers are written as the product of prime factors. The lowest common multiple will be the product of the all prime factors with the highest degree (power).
Example 1:
Find the LCM of 20 and 12 by prime factorization method.
Solution:
Step 1: To find LCM of 20 and 12 write each number as a product of prime factors. 20=2×2×5=22×512=2×2×3=22×3
Step 2: Multiply all the prime factors with the highest degree.
Here we have 2 with highest power 2 and other prime factors 3 and 5. Multiply all these to get LCM.
LCM of 20 and 12 = 2×2×3×5=22×3×5=60
LCM by Division Method
\ In this method divide the given numbers by common prime number until the remainder is a prime number or one. LCM will be the product obtained by multiplying all divisors and remaining prime numbers.
Example 2:
Find the LCM of 24 and 15 by division method.
Solution:
Step 1: Divide the given numbers by the least prime number.
Here, 2 is the least number which will divide 24.
Division Method
Step 2: Write the quotient and the number which is not divisible by the above prime number in the second row.
In the second row, write the quotient we get after the division of 24 by 2. Since 15 is not divisible by 2 write 15 in the second row as it is.
LCM
Step 3: Divide the numbers with another least prime number.
Step 4: Continue division until the remainder is a prime number or 1.
Prime Factorization Method
Step 5: Multiply all the divisors and remaining prime number (if any) to obtain the LCM.
LCM of 24 and 15= 2×2×2×3×5=23×3×5=120
HCF By Prime Factorization Method
Given natural numbers are written as the product of prime factors. To obtain the highest common factor multiply all the common prime factors with the lowest degree (power).
Example 1:
Find the HCF of 20 and 12 by prime factorization method.
Solution:
LCM by Division MethodPrime Factorization
Step-by-step explanation:
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