LCM of 30 and 42
LCM of 30 and 42 is the smallest number among all common multiples of 30 and 42. The first few multiples of 30 and 42 are (30, 60, 90, 120, . . . ) and (42, 84, 126, 168, 210, 252, 294, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 42  by division method, by prime factorization, and by listing multiples.
1.  LCM of 30 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 30 and 42?
Answer: LCM of 30 and 42 is 210.
Explanation:
The LCM of two nonzero integers, x(30) and y(42), is the smallest positive integer m(210) that is divisible by both x(30) and y(42) without any remainder.
Methods to Find LCM of 30 and 42
The methods to find the LCM of 30 and 42 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 30 and 42 by Prime Factorization
Prime factorization of 30 and 42 is (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1} and (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} respectively. LCM of 30 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 5^{1} × 7^{1} = 210.
Hence, the LCM of 30 and 42 by prime factorization is 210.
LCM of 30 and 42 by Division Method
To calculate the LCM of 30 and 42 by the division method, we will divide the numbers(30, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 42.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 42. Write this prime number(2) on the left of the given numbers(30 and 42), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (30, 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 30 and 42 is the product of all prime numbers on the left, i.e. LCM(30, 42) by division method = 2 × 3 × 5 × 7 = 210.
LCM of 30 and 42 by Listing Multiples
To calculate the LCM of 30 and 42 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 30 (30, 60, 90, 120, . . . ) and 42 (42, 84, 126, 168, 210, 252, 294, . . . . )
 Step 2: The common multiples from the multiples of 30 and 42 are 210, 420, . . .
 Step 3: The smallest common multiple of 30 and 42 is 210.
∴ The least common multiple of 30 and 42 = 210.
☛ Also Check:
 LCM of 18 and 63  126
 LCM of 9 and 13  117
 LCM of 4, 9 and 10  180
 LCM of 12, 16 and 20  240
 LCM of 24 and 45  360
 LCM of 12 and 42  84
 LCM of 13 and 52  52
LCM of 30 and 42 Examples

Example 1: The GCD and LCM of two numbers are 6 and 210 respectively. If one number is 30, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 30 × y
⇒ y = (GCD × LCM)/30
⇒ y = (6 × 210)/30
⇒ y = 42
Therefore, the other number is 42. 
Example 2: The product of two numbers is 1260. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 1260
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1260/6
Therefore, the LCM is 210.
The probable combination for the given case is LCM(30, 42) = 210. 
Example 3: Verify the relationship between GCF and LCM of 30 and 42.
Solution:
The relation between GCF and LCM of 30 and 42 is given as,
LCM(30, 42) × GCF(30, 42) = Product of 30, 42
Prime factorization of 30 and 42 is given as, 30 = (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1} and 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1}
LCM(30, 42) = 210
GCF(30, 42) = 6
LHS = LCM(30, 42) × GCF(30, 42) = 210 × 6 = 1260
RHS = Product of 30, 42 = 30 × 42 = 1260
⇒ LHS = RHS = 1260
Hence, verified.
FAQs on LCM of 30 and 42
What is the LCM of 30 and 42?
The LCM of 30 and 42 is 210. To find the LCM (least common multiple) of 30 and 42, we need to find the multiples of 30 and 42 (multiples of 30 = 30, 60, 90, 120 . . . . 210; multiples of 42 = 42, 84, 126, 168 . . . . 210) and choose the smallest multiple that is exactly divisible by 30 and 42, i.e., 210.
If the LCM of 42 and 30 is 210, Find its GCF.
LCM(42, 30) × GCF(42, 30) = 42 × 30
Since the LCM of 42 and 30 = 210
⇒ 210 × GCF(42, 30) = 1260
Therefore, the greatest common factor (GCF) = 1260/210 = 6.
What are the Methods to Find LCM of 30 and 42?
The commonly used methods to find the LCM of 30 and 42 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
What is the Relation Between GCF and LCM of 30, 42?
The following equation can be used to express the relation between GCF and LCM of 30 and 42, i.e. GCF × LCM = 30 × 42.
How to Find the LCM of 30 and 42 by Prime Factorization?
To find the LCM of 30 and 42 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (42 = 2 × 3 × 7). LCM of 30 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 42.
⇒ LCM of 30, 42 = 2^{1} × 3^{1} × 5^{1} × 7^{1} = 210.
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