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Last updated on September 13th, 2024
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 8 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
The LCM of 8 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below
The LCM of 8 and 10 can be found using the following steps:
Steps:
1. Write down the multiples of each number
Multiples of 8: 8, 16, 24, 32, 40, …
Multiples of 10: 10, 20, 30, 40, …
2. Ascertain the smallest multiple from the listed multiples
The smallest common multiple of 8 and 10 is 40.
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of each number:
Prime factorization of 8 = 2×2×2
Prime factorization of 10 = 2×5
2. Take the highest powers of each prime factor:
Highest power of 2: 23
Highest power of 5: 51
3. Multiply the highest powers to find the LCM:
LCM(8, 10) = 40
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers
2. Divide by prime factors:
3. Multiply the divisors:
2×2×2×5=40
So, LCM(8, 10) = 40