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
