LCM of 9 and 42
LCM of 9 and 42 is the smallest number among all common multiples of 9 and 42. The first few multiples of 9 and 42 are (9, 18, 27, 36, 45, . . . ) and (42, 84, 126, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 42  by division method, by prime factorization, and by listing multiples.
1.  LCM of 9 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 9 and 42?
Answer: LCM of 9 and 42 is 126.
Explanation:
The LCM of two nonzero integers, x(9) and y(42), is the smallest positive integer m(126) that is divisible by both x(9) and y(42) without any remainder.
Methods to Find LCM of 9 and 42
Let's look at the different methods for finding the LCM of 9 and 42.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 9 and 42 by Division Method
To calculate the LCM of 9 and 42 by the division method, we will divide the numbers(9, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 42.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 42. Write this prime number(2) on the left of the given numbers(9 and 42), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (9, 42) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 9 and 42 is the product of all prime numbers on the left, i.e. LCM(9, 42) by division method = 2 × 3 × 3 × 7 = 126.
LCM of 9 and 42 by Listing Multiples
To calculate the LCM of 9 and 42 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, . . . ) and 42 (42, 84, 126, 168, . . . . )
 Step 2: The common multiples from the multiples of 9 and 42 are 126, 252, . . .
 Step 3: The smallest common multiple of 9 and 42 is 126.
∴ The least common multiple of 9 and 42 = 126.
LCM of 9 and 42 by Prime Factorization
Prime factorization of 9 and 42 is (3 × 3) = 3^{2} and (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} respectively. LCM of 9 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 7^{1} = 126.
Hence, the LCM of 9 and 42 by prime factorization is 126.
☛ Also Check:
 LCM of 7 and 49  49
 LCM of 4, 9 and 10  180
 LCM of 10 and 24  120
 LCM of 30 and 54  270
 LCM of 8, 15 and 20  120
 LCM of 3, 5 and 8  120
 LCM of 2, 5 and 8  40
LCM of 9 and 42 Examples

Example 1: Find the smallest number that is divisible by 9 and 42 exactly.
Solution:
The smallest number that is divisible by 9 and 42 exactly is their LCM.
⇒ Multiples of 9 and 42: Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, . . . .
 Multiples of 42 = 42, 84, 126, 168, 210, . . . .
Therefore, the LCM of 9 and 42 is 126.

Example 2: Verify the relationship between GCF and LCM of 9 and 42.
Solution:
The relation between GCF and LCM of 9 and 42 is given as,
LCM(9, 42) × GCF(9, 42) = Product of 9, 42
Prime factorization of 9 and 42 is given as, 9 = (3 × 3) = 3^{2} and 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1}
LCM(9, 42) = 126
GCF(9, 42) = 3
LHS = LCM(9, 42) × GCF(9, 42) = 126 × 3 = 378
RHS = Product of 9, 42 = 9 × 42 = 378
⇒ LHS = RHS = 378
Hence, verified. 
Example 3: The product of two numbers is 378. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 378
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 378/3
Therefore, the LCM is 126.
The probable combination for the given case is LCM(9, 42) = 126.
FAQs on LCM of 9 and 42
What is the LCM of 9 and 42?
The LCM of 9 and 42 is 126. To find the LCM (least common multiple) of 9 and 42, we need to find the multiples of 9 and 42 (multiples of 9 = 9, 18, 27, 36 . . . . 126; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 9 and 42, i.e., 126.
What is the Relation Between GCF and LCM of 9, 42?
The following equation can be used to express the relation between GCF and LCM of 9 and 42, i.e. GCF × LCM = 9 × 42.
If the LCM of 42 and 9 is 126, Find its GCF.
LCM(42, 9) × GCF(42, 9) = 42 × 9
Since the LCM of 42 and 9 = 126
⇒ 126 × GCF(42, 9) = 378
Therefore, the greatest common factor (GCF) = 378/126 = 3.
How to Find the LCM of 9 and 42 by Prime Factorization?
To find the LCM of 9 and 42 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (42 = 2 × 3 × 7). LCM of 9 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 42.
⇒ LCM of 9, 42 = 2^{1} × 3^{2} × 7^{1} = 126.
Which of the following is the LCM of 9 and 42? 35, 32, 126, 10
The value of LCM of 9, 42 is the smallest common multiple of 9 and 42. The number satisfying the given condition is 126.
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