LCM of 42 and 49
LCM of 42 and 49 is the smallest number among all common multiples of 42 and 49. The first few multiples of 42 and 49 are (42, 84, 126, 168, 210, 252, 294, . . . ) and (49, 98, 147, 196, 245, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 49  by prime factorization, by division method, and by listing multiples.
1.  LCM of 42 and 49 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 42 and 49?
Answer: LCM of 42 and 49 is 294.
Explanation:
The LCM of two nonzero integers, x(42) and y(49), is the smallest positive integer m(294) that is divisible by both x(42) and y(49) without any remainder.
Methods to Find LCM of 42 and 49
Let's look at the different methods for finding the LCM of 42 and 49.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 42 and 49 by Prime Factorization
Prime factorization of 42 and 49 is (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and (7 × 7) = 7^{2} respectively. LCM of 42 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 7^{2} = 294.
Hence, the LCM of 42 and 49 by prime factorization is 294.
LCM of 42 and 49 by Listing Multiples
To calculate the LCM of 42 and 49 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, 252, 294, . . . ) and 49 (49, 98, 147, 196, 245, . . . . )
 Step 2: The common multiples from the multiples of 42 and 49 are 294, 588, . . .
 Step 3: The smallest common multiple of 42 and 49 is 294.
∴ The least common multiple of 42 and 49 = 294.
LCM of 42 and 49 by Division Method
To calculate the LCM of 42 and 49 by the division method, we will divide the numbers(42, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 49.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 49. Write this prime number(2) on the left of the given numbers(42 and 49), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (42, 49) 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 42 and 49 is the product of all prime numbers on the left, i.e. LCM(42, 49) by division method = 2 × 3 × 7 × 7 = 294.
☛ Also Check:
 LCM of 15, 30 and 90  90
 LCM of 40, 42 and 45  2520
 LCM of 6 and 14  42
 LCM of 6 and 10  30
 LCM of 2 and 3  6
 LCM of 3 and 15  15
 LCM of 20 and 50  100
LCM of 42 and 49 Examples

Example 1: The product of two numbers is 2058. If their GCD is 7, what is their LCM?
Solution:
Given: GCD = 7
product of numbers = 2058
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2058/7
Therefore, the LCM is 294.
The probable combination for the given case is LCM(42, 49) = 294. 
Example 2: Find the smallest number that is divisible by 42 and 49 exactly.
Solution:
The smallest number that is divisible by 42 and 49 exactly is their LCM.
⇒ Multiples of 42 and 49: Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, . . . .
 Multiples of 49 = 49, 98, 147, 196, 245, 294, 343, . . . .
Therefore, the LCM of 42 and 49 is 294.

Example 3: The GCD and LCM of two numbers are 7 and 294 respectively. If one number is 49, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 49 × z
⇒ z = (GCD × LCM)/49
⇒ z = (7 × 294)/49
⇒ z = 42
Therefore, the other number is 42.
FAQs on LCM of 42 and 49
What is the LCM of 42 and 49?
The LCM of 42 and 49 is 294. To find the LCM (least common multiple) of 42 and 49, we need to find the multiples of 42 and 49 (multiples of 42 = 42, 84, 126, 168 . . . . 294; multiples of 49 = 49, 98, 147, 196 . . . . 294) and choose the smallest multiple that is exactly divisible by 42 and 49, i.e., 294.
If the LCM of 49 and 42 is 294, Find its GCF.
LCM(49, 42) × GCF(49, 42) = 49 × 42
Since the LCM of 49 and 42 = 294
⇒ 294 × GCF(49, 42) = 2058
Therefore, the greatest common factor = 2058/294 = 7.
Which of the following is the LCM of 42 and 49? 50, 10, 2, 294
The value of LCM of 42, 49 is the smallest common multiple of 42 and 49. The number satisfying the given condition is 294.
How to Find the LCM of 42 and 49 by Prime Factorization?
To find the LCM of 42 and 49 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (49 = 7 × 7). LCM of 42 and 49 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 49.
⇒ LCM of 42, 49 = 2^{1} × 3^{1} × 7^{2} = 294.
What is the Relation Between GCF and LCM of 42, 49?
The following equation can be used to express the relation between GCF and LCM of 42 and 49, i.e. GCF × LCM = 42 × 49.
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