In 2020, the World Health Organization (WHO) launched a strategy to eliminate cervical cancer as a public health problem. To support the strategy, the WHO published updated cervical screening guidelines in 2021. To inform this update, we used an established modeling platform, Policy1-Cervix, to evaluate the impact of seven primary screening scenarios across 78 low- and lower-middle-income countries (LMICs) for the general population of women. Assuming 70% coverage, we found that primary human papillomavirus (HPV) screening approaches were the most effective and cost-effective, reducing cervical cancer age-standardized mortality rates by 63-67% when offered every 5 years. Strategies involving triaging women before treatment (with 16/18 genotyping, cytology, visual inspection with acetic acid (VIA) or colposcopy) had close-to-similar effectiveness to HPV screening without triage and fewer pre-cancer treatments. Screening with VIA or cytology every 3 years was less effective and less cost-effective than HPV screening every 5 years. Furthermore, VIA generated more than double the number of pre-cancer treatments compared to HPV. In conclusion, primary HPV screening is the most effective, cost-effective and efficient cervical screening option in LMICs. These findings have directly informed WHO's updated cervical screening guidelines for the general population of women, which recommend primary HPV screening in a screen-and-treat or screen-triage-and-treat approach, starting from age 30 years with screening every 5 years or 10 years.