LCM of 2, 3, 4, and 5 is the smallest number among all common multiples of 2, 3, 4, and 5. The first few multiples of 2, 3, 4, and 5 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), and (5, 10, 15, 20, 25 . . .) respectively. There are 3 commonly used methods to find LCM of 2, 3, 4, 5 - by prime factorization, by division method, and by listing multiples.
1. LCM of 2, 3, 4, and 5 2. List of Methods 3. Solved Examples 4. FAQsAnswer: LCM of 2, 3, 4, and 5 is 60.
Explanation:
The LCM of four non-zero integers, a(2), b(3), c(4), and d(5), is the smallest positive integer m(60) that is divisible by a(2), b(3), c(4), and d(5) without any remainder.
Let's look at the different methods for finding the LCM of 2, 3, 4, and 5.
- By Listing Multiples
- By Prime Factorization Method
- By Division Method
LCM of 2, 3, 4, and 5 by Listing Multiples
To calculate the LCM of 2, 3, 4, 5 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 2 (2, 4, 6, 8, 10 . . .), 3 (3, 6, 9, 12, 15 . . .), 4 (4, 8, 12, 16, 20 . . .), and 5 (5, 10, 15, 20, 25 . . .).
- Step 2: The common multiples from the multiples of 2, 3, 4, and 5 are 60, 120, . . .
- Step 3: The smallest common multiple of 2, 3, 4, and 5 is 60.
∴ The least common multiple of 2, 3, 4, and 5 = 60.
LCM of 2, 3, 4, and 5 by Prime Factorization
Prime factorization of 2, 3, 4, and 5 is (2) = 21, (3) = 31, (2 × 2) = 22, and (5) = 51 respectively. LCM of 2, 3, 4, and 5 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60. Hence, the LCM of 2, 3, 4, and 5 by prime factorization is 60.
LCM of 2, 3, 4, and 5 by Division Method
To calculate the LCM of 2, 3, 4, and 5 by the division method, we will divide the numbers(2, 3, 4, 5) by their prime factors (preferably common). The product of these divisors gives the LCM of 2, 3, 4, and 5.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2, 3, 4, and 5. Write this prime number(2) on the left of the given numbers(2, 3, 4, and 5), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (2, 3, 4, 5) 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 2, 3, 4, and 5 is the product of all prime numbers on the left, i.e. LCM(2, 3, 4, 5) by division method = 2 × 2 × 3 × 5 = 60.
☛ Also Check:
- LCM of 40, 56 and 60 - 840
- LCM of 30 and 50 - 150
- LCM of 90 and 105 - 630
- LCM of 9 and 18 - 18
- LCM of 18 and 63 - 126
- LCM of 100 and 190 - 1900
- LCM of 8, 15 and 21 - 840
