You are given that 270 = 3³ × 2 × 5 and 177 147 = 3¹¹ (a) (i) Find the lowest common multiple (LCM) of 270 and 177 147 - OCR - GCSE Maths - Question 11 - 2019 - Paper 6

Given the number: 177 147 000 000, we can express it as follows:

First, recognize that this number can be rewritten with prime factors: $177 147 000 000 = 177 147 imes 10^{6}$

Breaking down $10^{6}$, we have: $10^6 = (2^1 imes 5^1)^{6} = 2^6 imes 5^6$

Next, using the prime factorization for 177 147, $177 147 = 3^{11}$

Thus, we combine these together:

$177 147 000 000 = 3^{11} imes 2^6 imes 5^6$

From the equation: $3^n = 177147 \times 9^5$

First, note that $9^5 = (3^2)^5 = 3^{10}$.

Thus, we have: $3^n = 177147 \times 3^{10}$

Recalling that $177 147 = 3^{11}$, we rewrite it: $3^n = 3^{11} \times 3^{10}$

Combine the powers: $3^n = 3^{21}$

From the property of exponents, we equate exponents: $n = 21$