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185 LearnersLast updated on November 29th, 2024
LCM of 42 and 66
The LCM is the smallest number which can be exactly divisible by each of the numbers. It can also be defined as the least number, which is a common multiple of all numbers. LCM helps in scheduling, also used in traffic light mechanisms, etc
What is the LCM of 42 and 66
The LCM of 42 and 66 is 462. We can get the exact value of LCM of 42 and 66 through various methods. Let us see how.
How to find the LCM of 42 and 66
To find the LCM of 42 and 66 we will learn some methods:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 42 and 66 Using Listing the Multiples
Listing Multiples method is one of the methods used to find LCM of some given numbers. We have to know the multiples of the given numbers and then apply this method.
Step 1:List down the multiples of each number
Multiples of 42 = 42,84,126,168,210,252,294,336,378,420,462,504,.....
Multiples of 66= 66,132,198,264,330,396,462,528,594,....
Step 2: Find out the smallest multiple from the listed multiple
The smallest common multiple is 462
Thus, LCM (42,66) = 462.
LCM of 42 and 66 Using Prime Factorization
Rule: The prime factorization of each number is to be done, and then the highest power of the prime factors are multiplied to get the LCM.
Step 1: Find the prime factorization of the numbers:
Prime factorization of 42 = 2×3×7
Prime factorization of 66 = 2×3×11
Step 1:Take the highest powers of each prime factor, and multiply the highest powers to
get the LCM:
2×3×7×11 = 462
LCM (42,66) = 462.
LCM of 42 and 66 Using Division Method
This is the most used method to find any LCM. It involves dividing both numbers 42 and 66 by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM
Step 1: Write the numbers, divide by common prime factors. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
The first common prime divisors for both 42 and 66 are 2 and 3. We choose 2.
Step 2: Dividing 42 and 66 with 2, we get 21 and 33 respectively.
Step 3: Repeat Step 1 and 2 till both are getting perfectly divided. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
2×3×7×11 = 462
Thus, LCM (42,66) = 462
Common Mistakes and How to Avoid Them in LCM of 42 and 66
LCM of 42 and 66 Examples
Problem 1
The LCM of two numbers is 462 and the numbers are in the ratio 7:11. Find the numbers.
Explanation
Problem 2
LCM (42,66) = x. Find the smallest positive integer (n), where n×x=231.
Explanation
Problem 3
What is the LCM of 12 and 18?
Explanation
FAQs on LCM of 42 and 66
1.What is the LCM of 46 and 66?
2.What is the LCM of 44 and 66 ?
3.What is the LCM of 40 and 66?
4.How to calculate LCM?
Important glossaries for the LCM of 42 and 66
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
