Question

Find the L.C.M of the given pair of numbers using the prime factors method. 70 and 84​

Answer 1

2| 70,84

2|35,42

3|35,21

5|35,7

.|5,7

LCM=2×2×3×5×5×7=2100

Answer 2

Answer:

420

Step-by-step explanation:

Prime Number: a whole number greater than 1 that cannot be made by multiplying other whole numbers

First prime numbers: 2, 3, 5, 7, 11, 13, 17, ...

Prime Factorization: prime numbers that multiply together to make the original number.

LCM = least common multiple: smallest positive number that is a multiple of two or more numbers

Start by finding the prime factorization of each number.

Start with the smallest prime number: 2

70 ÷ 2 = 35

35 is not divisible by 2 or 3, but is divisible by 5:

35 ÷ 5 = 7

7 is a prime number, so cannot be divided any further

So  70 = 2 × 5 × 7

Start with the smallest prime number: 2

84 ÷ 2 = 42

Again divide by 2:

42 ÷ 2 = 21

Now divide by 3:

21 ÷ 3 = 7

So  84 = 2 × 2 × 3 × 7

Write each number as a product of primes, matching primes vertically when possible

84 = 2 × 2 × 3       × 7

70 = 2             × 5 × 7

Now bring down the primes in each column. The LCM is the product of these factors.

LCM = 2 × 2 × 3 × 5 × 7 = 420